<PAGE>   1
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                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-Q

[X]        QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                For the quarterly period ended September 30, 1998

                                       OR

[ ]        TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
                       For the transition period from        to 
                                                      ------    ------

                         Commission file number 1-10934

                        LAKEHEAD PIPE LINE PARTNERS, L.P.
             (Exact name of Registrant as specified in its charter)


                     DELAWARE                            39-1715850
          (State or other jurisdiction of              (I.R.S. Employer
          incorporation or organization)              Identification No.)

                              LAKE SUPERIOR PLACE
                             21 WEST SUPERIOR STREET
                              DULUTH, MN 55802-2067
              (Address of principal executive offices and zip code)

                                 (218) 725-0100
              (Registrant's telephone number, including area code )

                             ------------------------

Indicate by check mark whether the Registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the Registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes  X  No
                                       ---    ---

The Registrant had 22,290,000 Class A Common Units outstanding as at November
12, 1998.
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                               TABLE OF CONTENTS
<TABLE>
<CAPTION>


                                                                                                               PAGE

                          PART I. FINANCIAL INFORMATION

<S>            <C>                                                                                              <C>
ITEM 1.         Financial Statements

                  Consolidated Statement of Income
                    for the three month and nine month periods ended September 30, 1998 and 1997...........       1

                  Consolidated Statement of Cash Flows
                    for the nine month periods ended September 30, 1998 and 1997...........................       2

                  Consolidated Statement of Financial Position
                    as at September 30, 1998 and December 31, 1997.........................................       3

                  Consolidated Statement of Partners' Capital
                    for the nine months ended September 30, 1998...........................................       4

                  Notes to the Consolidated Financial Statements...........................................       4


ITEM 2.         Management's Discussion and Analysis of
                  Financial Condition and Results of Operations............................................       6


                           PART II. OTHER INFORMATION

ITEM 1.         Legal Proceedings..........................................................................      12

ITEM 6.         Exhibits and Reports on Form 8-K...........................................................      13

SIGNATURE     .............................................................................................      14
</TABLE>

     This Quarterly Report on Form 10-Q contains forward-looking statements and
information that are based on the beliefs of the Partnership as well as
assumptions made by and information currently available to the Partnership. When
used in this document, the words "anticipate," "believe," "expect," "estimate,"
"forecast," "project," and similar expressions are intended to identify
forward-looking statements. Such statements reflect the Partnership's current
views with respect to future events and are subject to certain risks,
uncertainties and assumptions including the Partnership's ability to complete
expansion programs on time and within budget and to recover the costs of such
expansions in its tariffs. Should one or more risks or uncertainties
materialize, or should underlying assumptions prove incorrect, actual results
may vary materially from those anticipated, believed, expected, estimated,
forecasted, or projected. Except as required by applicable securities laws, the
Partnership does not intend to update these forward-looking statements and
information. For additional discussion of such risks, uncertainties and
assumptions, see the Partnership's 1997 Annual Report on Form 10-K and Form
10-K/A.
<PAGE>   3
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PART I - FINANCIAL INFORMATION
--------------------------------------------------------------------------------

ITEM 1.  FINANCIAL STATEMENTS
--------------------------------------------------------------------------------

                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                        CONSOLIDATED STATEMENT OF INCOME

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>

                                                                      Three months ended         Nine months ended
                                                                          September 30,             September 30,
 (unaudited; dollars in millions, except per Unit amounts)             1998         1997         1998          1997
---------------------------------------------------------------------------------------------------------------------

<S>                                                               <C>           <C>            <C>          <C>      
Operating Revenue                                                 $    70.2     $     72.3     $  217.5     $   207.9
---------------------------------------------------------------------------------------------------------------------


Expenses
   Power                                                               16.1           16.2         52.7          48.0
   Operating and administrative                                        16.5           19.2         49.8          50.9
   Depreciation                                                        10.4            9.8         31.2          29.3
---------------------------------------------------------------------------------------------------------------------


                                                                       43.0           45.2        133.7         128.2
---------------------------------------------------------------------------------------------------------------------

Operating Income                                                       27.2           27.1         83.8          79.7

Interest and Other Income                                               0.6            2.0          4.7           7.1

Interest Expense                                                       (5.0)          (9.5)       (18.0)         29.8)

Minority Interest                                                      (0.2)          (0.2)        (0.8)         (0.7)
---------------------------------------------------------------------------------------------------------------------


Net Income                                                        $    22.6     $     19.4     $   69.7     $    56.3
=====================================================================================================================



Net Income Per Unit (Note 3)                                      $    0.78     $     0.76     $   2.43     $    2.22
=====================================================================================================================



Cash Distributions Paid Per Unit (Note 4)                         $    0.86     $     0.78     $   2.50     $    2.14
=====================================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.

                                       1
<PAGE>   4


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                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                      CONSOLIDATED STATEMENT OF CASH FLOWS

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                                                  Nine months ended
                                                                                                    September 30,
(unaudited; dollars in millions)                                                                 1998          1997
--------------------------------------------------------------------------------------------------------------------

<S>                                                                                          <C>            <C>
Operating Activities
   Net income                                                                                $   69.7        $ 56.3
   Adjustments to reconcile net income to
     cash provided from operating activities:
        Depreciation                                                                             31.2          29.3
        Interest on accrued rate refunds (Note 5)                                                 1.7           2.8
        Other                                                                                     0.6           1.1
        Changes in operating assets and liabilities:
           Accounts receivable and other                                                          3.0           6.1
           Materials and supplies                                                                (0.3)         (0.2)
           General Partner and affiliates                                                         2.1          (0.2)
           Accounts payable and other                                                             1.9          (0.3)
           Interest payable                                                                       3.5           8.8
           Property and other taxes                                                              (1.6)         (1.0)
           Payment of rate refunds and related interest (Note 5)                                (21.5)        (20.4)
-------------------------------------------------------------------------------------------------------------------


                                                                                                 90.3          82.3
-------------------------------------------------------------------------------------------------------------------


Investing Activities
   Additions to property, plant and equipment                                                  (351.4)        (79.5)
   Short-term investments, net                                                                   48.9          29.5
   Advances to affiliate                                                                        (19.9)           --
-------------------------------------------------------------------------------------------------------------------

                                                                                               (322.4)        (50.0)
-------------------------------------------------------------------------------------------------------------------


Financing Activities
   Issuance of variable rate financing                                                          187.0            --
   Loan from General Partner                                                                     37.0            --
   Distributions to partners                                                                    (70.8)        (53.5)
   Minority interest                                                                             (0.7)         (0.6)
   Other                                                                                         (0.3)           --
-------------------------------------------------------------------------------------------------------------------

                                                                                                152.2         (54.1)
-------------------------------------------------------------------------------------------------------------------

Decrease in Cash and Cash Equivalents *                                                         (79.9)        (21.8)

Cash and Cash Equivalents at Beginning of Period                                                118.6          89.6
-------------------------------------------------------------------------------------------------------------------


Cash and Cash Equivalents at End of Period                                                   $   38.7        $ 67.8
===================================================================================================================
</TABLE>

*  Cash equivalents are defined as all highly marketable securities with a
   maturity of three months or less when purchased. Short-term investments are
   those marketable securities which have a maturity of more than three months
   but less than twelve months when purchased.

See accompanying notes to the consolidated financial statements.

                                       2
<PAGE>   5


--------------------------------------------------------------------------------

                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                  CONSOLIDATED STATEMENT OF FINANCIAL POSITION

--------------------------------------------------------------------------------
<TABLE>
<CAPTION>


                                                                                      September 30,       December 31,
(unaudited, except for December 31, 1997; dollars in millions)                             1998               1997
----------------------------------------------------------------------------------------------------------------------

                                     ASSETS
<S>                                                                                 <C>                 <C>           
Current Assets
   Cash and cash equivalents                                                        $      38.7         $        118.6
   Short-term investments                                                                   5.0                   53.9
   Due from General Partner and affiliates                                                  0.5                    2.6
   Advances to affiliate                                                                   19.9                     --
   Accounts receivable and other                                                           19.4                   22.4
   Materials and supplies                                                                   7.4                    7.1
----------------------------------------------------------------------------------------------------------------------

                                                                                           90.9                  204.6
----------------------------------------------------------------------------------------------------------------------

Deferred Charges and Other                                                                  4.9                    4.4
----------------------------------------------------------------------------------------------------------------------

Property, Plant and Equipment
   At cost                                                                              1,353.9                1,008.5
   Accumulated depreciation                                                              (183.4)                (158.2)
----------------------------------------------------------------------------------------------------------------------

                                                                                        1,170.5                 850.3
----------------------------------------------------------------------------------------------------------------------

                                                                                    $   1,266.3         $      1,059.3
======================================================================================================================
                        LIABILITIES AND PARTNERS' CAPITAL
Current Liabilities
   Accounts payable and other                                                       $      22.1         $         20.2
   Interest payable                                                                         8.8                    5.3
   Property and other taxes                                                                 9.8                   11.4
   Current portion of accrued rate refunds and related interest (Note 5)                   29.0                   29.0
----------------------------------------------------------------------------------------------------------------------

                                                                                           69.7                   65.9

Long-Term Debt                                                                            650.0                  463.0
Loan from General Partner                                                                  37.0                     --
Accrued Rate Refunds and Related Interest (Note 5)                                          6.3                   26.1
Minority Interest                                                                           2.6                    2.5
Contingencies (Note 6)
----------------------------------------------------------------------------------------------------------------------

                                                                                          765.6                  557.5
----------------------------------------------------------------------------------------------------------------------

Partners' Capital
   Class A Common Unitholders (Units authorized and issued - 22,290,000)                  458.6                  461.6
   Class B Common Unitholder (Units authorized and issued - 3,912,750)                     37.8                   36.7
   General Partner                                                                          4.3                    3.5
----------------------------------------------------------------------------------------------------------------------

                                                                                          500.7                  501.8
----------------------------------------------------------------------------------------------------------------------

                                                                                    $   1,266.3         $      1,059.3
======================================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.

                                       3
<PAGE>   6
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                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                   CONSOLIDATED STATEMENT OF PARTNERS' CAPITAL

--------------------------------------------------------------------------------

<TABLE>
<CAPTION>

                                                       Class A               Class B
(unaudited, except for December 31, 1997;               Common                Common       General
 dollars in millions)                              Unitholders            Unitholder       Partner             Total
----------------------------------------------------------------------------------------------------------------------


<S>                                                 <C>                    <C>            <C>             <C>   
Partners' Capital at December 31, 1997               $   461.6              $   36.7       $   3.5         $     501.8

Net Income Allocation                                     52.8                  10.9           6.0                69.7

Distributions to Partners                                (55.8)                 (9.8)         (5.2)              (70.8)
----------------------------------------------------------------------------------------------------------------------


Partners' Capital at September 30, 1998              $   458.6                 $37.8       $   4.3         $     500.7

======================================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.


--------------------------------------------------------------------------------

           NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS (UNAUDITED)

--------------------------------------------------------------------------------

1.   Basis of Presentation

     The accompanying unaudited consolidated financial statements have been
     prepared in accordance with United States generally accepted accounting
     principles for interim financial information and with the instructions to
     Form 10-Q and Rule 10-01 of Regulation S-X. Accordingly, they do not
     include all the information and footnotes required by generally accepted
     accounting principles for complete financial statements. In the opinion of
     management, they contain all adjustments which management considers
     necessary to present fairly the financial position as at September 30, 1998
     and December 31, 1997; the results of operations for the three and nine
     month periods ended September 30, 1998 and 1997; and cash flows for the
     nine month periods ended September 30, 1998 and 1997. The results of
     operations for the three months and nine months ended September 30, 1998
     should not be taken as indicative of the results to be expected for the
     full year. The interim financial statements should be read in conjunction
     with the Partnership's consolidated financial statements and notes thereto
     presented in the Partnership's 1997 Annual Report on Form 10-K and Form
     10-K/A.

2.   Comprehensive Income

     Statement of Financial Accounting Standards No. 130, "Reporting
     Comprehensive Income," became effective for fiscal years beginning after
     December 15, 1997. Comprehensive income is defined as "the change in equity
     of a business enterprise during a period from transactions and other events
     and circumstances from nonowner sources. It includes all changes in equity
     during a period except those resulting from investments by owners and
     distributions to owners."

     "Comprehensive Income" encompasses "Net Income" and other revenues,
     expenses, gains, and losses that under generally accepted accounting
     principles are included in comprehensive income but excluded from net
     income. These other components of comprehensive income include foreign
     currency translation adjustments and unrealized holding gains and losses on
     available for sale securities. For the three month and nine month periods
     ended September 30, 1998 and 1997, the Partnership does not have any items
     of "other" comprehensive income. As such, the Partnership is not required
     to report comprehensive income in a separate financial statement.

                                       4
<PAGE>   7

3.   Net Income Per Unit

     Net income per unit is computed by dividing net income, after deduction of
     the General Partner's allocation, by the weighted average number of Class A
     and Class B Common Units outstanding. The General Partner's allocation is
     equal to an amount based upon its 1% general partner interest, adjusted to
     reflect an amount equal to incentive distributions and an amount required
     to reflect depreciation on the General Partner's historical cost basis for
     assets contributed on formation of the Partnership. Net income per unit was
     determined as follows:
<TABLE>
<CAPTION>

-------------------------------------------------------------------------------------------------------------------

                                                              Three months ended                 Nine months ended
     (unaudited; dollars in millions,                           September 30,                       September 30,
     except per Unit amounts)                                 1998          1997                 1998         1997
-------------------------------------------------------------------------------------------------------------------

<S>                                                       <C>          <C>                   <C>          <C>     
     Net income                                           $   22.6     $    19.4             $   69.7     $   56.3
-------------------------------------------------------------------------------------------------------------------

     Net income allocated to General Partner                  (0.2)         (0.2)                (0.7)        (0.6)

     Incentive distributions and
       historical cost depreciation adjustments               (1.8)         (1.0)                (5.3)        (2.4)
-------------------------------------------------------------------------------------------------------------------

                                                              (2.0)         (1.2)                (6.0)        (3.0)
-------------------------------------------------------------------------------------------------------------------

     Net income allocable to Common Units                 $   20.6     $    18.2             $   63.7     $   53.3
===================================================================================================================

     Common Units outstanding (millions)                      26.2          24.0                 26.2         24.0
===================================================================================================================

     Net income per unit                                  $   0.78     $    0.76             $   2.43     $   2.22
===================================================================================================================
</TABLE>


4.   Cash Distribution

     On October 15, 1998, the Board of Directors of the General Partner declared
     a cash distribution for the quarter ended September 30, 1998, of $0.86 per
     unit. The distribution will be made on November 13, 1998, to Unitholders of
     record on October 30, 1998.

5.   Accrued Rate Refunds and Related Interest

     In 1996, the Federal Energy Regulatory Commission ("FERC") approved a
     settlement agreement ("Settlement Agreement") between the Partnership and
     customer representatives on all then outstanding contested tariff rates.
     The Settlement Agreement resulted in an approximate tariff rate reduction
     of 6% and total rate refunds and related interest of $120.0 million through
     the effective date of October 1, 1996. The rate refund and related interest
     is being repaid through a 10% reduction in tariff rates and, at September
     30, 1998, the balance remaining was $35.3 million. This reduction will
     continue until all refunds have been made, which is expected to occur
     during the second half of 1999. Interest will continue to accrue on the
     unpaid rate refund balance based on the 90-day Treasury bill rate.

                                       5
<PAGE>   8
6.   Environmental Contingencies

     The Partnership is subject to federal and state laws and regulations
     relating to the protection of the environment. Environmental risk is
     inherent to liquid pipeline operations and the Partnership could, at times,
     be subject to environmental cleanup and enforcement actions. The General
     Partner manages this environmental risk through appropriate environmental
     policies and practices to minimize the impact to the Partnership. To the
     extent that the Partnership is unable to recover environmental costs in its
     rates (if not recovered through insurance), the General Partner has agreed
     to indemnify the Partnership from and against any costs relating to
     environmental liabilities associated with the pipeline system prior to its
     transfer to the Partnership in 1991. This excludes any liabilities
     resulting from a change in laws after such transfer. The Partnership
     continues to voluntarily investigate past leak sites for the purpose of
     assessing whether any remediation is required in light of current
     regulations, and to date no material environmental risks have been
     identified.


--------------------------------------------------------------------------------


ITEM 2.       MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND 
              RESULTS OF OPERATIONS

--------------------------------------------------------------------------------

RESULTS OF OPERATIONS

NINE MONTHS ENDED SEPTEMBER 30, 1998, COMPARED WITH NINE MONTHS ENDED SEPTEMBER 
30, 1997

Net income for the nine months ended September 30, 1998 was $69.7 million, or
$2.43 per unit, an increase of $13.4 million, or $0.21 per unit, over the same
period last year due to higher operating revenue and lower interest expense,
partially offset by higher operating expenses and lower interest and other
income.

Operating revenue increased $9.6 million, to $217.5 million, primarily due to
increased heavy crude oil deliveries. Deliveries averaged 1,575,000 barrels per
day for the first nine months of 1998, up 5% from the 1,496,000 averaged for the
first nine months of last year. Deliveries increased due to greater movement of
crude oil from western Canada into the Midwest U.S. and increased receipts of
crude oil in the Chicago, Illinois area for delivery to eastern Canada. System
utilization, measured in barrel miles, was 295 billion for the first nine months
of 1998, up 3% from the 287 billion for the first nine months of last year due
to increased deliveries. The increased system utilization reflects, in part, the
benefits of past pipeline expansion activities. The greater proportion of heavy
crude oil contributes additional revenue because the tariff rate for heavy crude
oil is greater than that for lighter crude oil due to the higher viscosity of
heavy crude oil which makes it more expensive to pump.

Total operating expenses for the first nine months of 1998 were $5.5 million
higher than the same period in 1997 due to increased power and depreciation
costs, partially offset by decreased operating and administrative costs. Power
costs increased $4.7 million primarily due to increased deliveries. Depreciation
expense increased $1.9 million due to growth in property, plant and equipment.
The decrease in operating and administrative costs of $1.1 million was due to
increased capitalized costs of $2.3 million associated with the Partnership's
System Expansion Program II ("SEP II"), offset by various cost increases
totaling $1.2 million.

Interest and other income for the first nine months of 1998 was $2.4 million
less than the same period in 1997 primarily due to lower interest income from
lower cash balances as a result of SEP II (see " - General, - SEP II Project")
and Terrace (see "- General, - Terrace Project") capital expenditures. Interest
expense for the first nine months of 1998 was $11.8 million less than the same
period in 1997 primarily due to increased capitalized interest in connection
with the SEP II and Terrace capital expenditures.

                                       6
<PAGE>   9
THREE MONTHS ENDED SEPTEMBER 30, 1998, COMPARED WITH THREE MONTHS ENDED 
SEPTEMBER 30, 1997

Net income for the three months ended September 30, 1998, was $22.6 million, or
$0.78 per unit, an increase of $3.2 million, or $0.02 per unit over the same
period last year, primarily due to decreased interest and operating expenses
partially offset by lower operating revenue and interest and other income.

Operating revenue decreased $2.1 million, to $70.2 million, due to a decrease in
the average length of haul during the third quarter of 1998 compared to the
third quarter of 1997. Total deliveries averaged 1,530,000 barrels per day for
the third quarter of 1998, approximately the same as the third quarter of 1997.
System utilization, measured in barrel miles, was 95 billion for the third
quarter of 1998, down 4% from 99 billion for the same period last year primarily
due to the decreased average length of haul. The decrease in average length of
haul is primarily attributable to increased receipts of crude oil in the Chicago
area for delivery to markets northeast of Chicago, including eastern Canada.

Total operating expenses for the three months ended September 30, 1998, were
$2.2 million less than the corresponding period in 1997, primarily due to a
decrease in operating and administrative costs of $2.7 million, partially offset
by the increase in depreciation costs of $0.6 million. Operating and
administrative costs decreased primarily due to lower pipeline internal
inspection costs in the third quarter of 1998 compared to the third quarter of
1997. Internal inspection costs decreased in the third quarter of 1998 due to
the timing of the 1998 internal inspections, which were largely completed in the
first half of the year. Depreciation expense increased due to growth in
property, plant and equipment.

Interest and other income decreased $1.4 million and interest expense decreased
$4.5 million in the third quarter of 1998 from the same period in 1997 for the
same reasons noted above in "Results of Operations, Nine Months Ended September
30, 1998, Compared with Nine Months Ended September 30, 1997."

The results of operations for the three month and nine month periods ended
September 30, 1998, should not be taken as indicative of the results of
operations expected for the full year.

LIQUIDITY AND CAPITAL RESOURCES

The General Partner believes that the Partnership will continue to have adequate
liquidity to fund future operating, investing and financing activities. The
Partnership intends to fund the remaining portion of SEP II (see " - General, -
SEP II Project"), Terrace (see " - General, - Terrace Project"), and ongoing
capital expenditures with the proceeds from future equity and debt offerings,
bank borrowings, cash generated from operating activities, and existing cash,
cash equivalents and short-term investments. Cash distributions are expected to
be funded with internally generated cash. The Partnership's ability to make
future equity and debt offerings and the timing of any such offerings will
depend on, among other factors, prevailing market conditions, interest rates and
the financial condition of the Partnership at the time of any such offering.

In keeping with its financing plans, the Partnership has utilized a portion of
its cash balance to finance its 1998 capital expenditures. Accordingly, at
September 30, 1998, cash, cash equivalents and short-term investments totaled
$43.7 million, down $128.8 million since December 31, 1997, as cash required for
distributions and capital expenditures exceeded cash generated from operating
activities and borrowings under the Partnership's Revolving Credit Facility. Of
this $43.7 million, $24.7 million (or $0.86 per unit) will be used for the cash
distribution payable November 13, 1998, with the remaining $19.0 million
available for capital expenditures or other business needs.

Cash flow from operating activities for the first nine months of 1998 increased
$8.0 million to $90.3 million from the corresponding period last year, due to
increased earnings, partially offset by an increase in working capital
requirements.

Capital expenditures for the first nine months of 1998 totaled $351.4 million,
of which $298.3 million was for the SEP II project which consists primarily of a
new pipeline from Superior, Wisconsin to the Chicago area. With $390.3 million
total SEP II 

                                       7
<PAGE>   10

costs incurred through September 30, 1998, the remaining SEP II costs of $59.7
million are expected to be incurred in the fourth quarter of 1998 and the first
quarter of 1999. In addition to SEP II, the Partnership anticipates spending
approximately $100 million on the Terrace expansion program, $11.0 million for
other pipeline system enhancements and $10.0 million for core maintenance
activities in 1998. Through September 30, 1998 approximately $42.4 million of
capital expenditures have been incurred on Terrace.

On July 22, 1998, Lakehead Pipe Line Company, Limited Partnership ("OLP"), the
operating partnership of which the Partnership is a 99% owner, filed a shelf
registration statement with the Securities and Exchange Commission for up to
$400.0 million of debt financing. On October 1, the Partnership issued $200
million of senior unsecured notes pursuant to this registration statement in two
tranches of $100 million each, with maturities of 2018 (with an interest rate of
7%) and 2028 (with an interest rate of 7.125%), respectively.

During the second quarter of 1998, the Board of Directors of the General Partner
approved an increase in the size of the Partnership's Revolving Credit Facility
from $205.0 million to $350.0 million in order to finance capital expenditures
(primarily SEP II), pending possible refinancing of borrowings under the
facility. In addition, certain covenants in the facility were modified to allow
additional borrowings by the Partnership. Interest rates charged on the facility
currently approximate 6%, and total borrowings under the facility were $340.0
million at September 30, 1998. In early October approximately $165 million of
this facility was repaid following the issuance of the $200 million of senior
unsecured notes by the OLP on October 1, 1998.

During the third quarter, the Board of Directors of the General Partner approved
a lending facility from the General Partner to the Partnership to provide an
alternative source of funds in the event that a disruption in the capital
markets delays anticipated debt and equity issuances. Under this facility, in
late September 1998, the Partnership borrowed $37.0 million from the General
Partner. This loan was repaid in early October upon completion of the OLP's
senior unsecured note offering.

The Partnership has entered into an easement acquisition agreement with Enbridge
Holdings (Mustang) Inc. ("Enbridge Mustang") (formerly IPL Patoka Pipeline
Holdings (U.S.A.) Inc.), an affiliate of the General Partner. Enbridge Mustang
is acquiring certain real property for the purpose of granting pipeline
easements to the Partnership in connection with SEP II. The Partnership has been
and will continue to make non-interest bearing cash advances to Enbridge Mustang
in order to provide for these real property acquisitions by Enbridge Mustang.


GENERAL

Year 2000 Computer Issue

The Year 2000 Readiness Program, which is being undertaken jointly by the
Partnership, the General Partner and its Enbridge affiliates, continued on
schedule, having attained several milestone points by September 30, 1998. The
year 2000 project management team has compiled a comprehensive list of all
computer hardware and software, embedded chip technologies and potentially
impacted business processes including those having significant third party
interdependencies. The team has also completed risk assessments and formulated
testing strategies for the items listed. The Partnership is currently involved
in various stages of implementing its year 2000 readiness initiatives and
expects to have all critical processes and assets compliant by mid 1999, at
which point lower risk systems will be remediated.

In order to address unforeseen year 2000 problems that could arise and in an
attempt to minimize business disruptions, the Partnership is developing business
contingency plans for all critical processes, systems, technologies and external
relationships. These plans are expected to be completed by mid 1999.

For additional discussion of the year 2000 issue, see the Partnership's Form
10-K/A (Amendment No. 1) filed September 15, 1998.

                                       8
<PAGE>   11

SEP II Rights-of-Way Acquisition and Permitting

In May 1997, the Illinois Commerce Commission ("ICC") denied the Partnership's
Application for a Certificate of Public Convenience and Necessity
("Certificate") for SEP II and the Illinois appellate courts have refused to
overturn this decision. Obtaining a Certificate is a first step in obtaining
eminent domain authority. Without condemnation authority, the cost to obtain
rights-of-way in connection with SEP II has increased and project completion has
been delayed. Nonetheless, the Partnership is continuing with its construction
of SEP II and the acquisition of rights-of-way through negotiation with
landowners.

SEP II Project

SEP II is more than 90% finished in Wisconsin, with the substantial completion
of the new Line 14. The Partnership has nearly completed pressure testing of
Line 14 in Wisconsin and is in the process of commissioning new pump stations.
The Partnership has commenced pipeline construction in all four Illinois
counties following receipt of the most significant construction permit from the
U.S. Army Corps of Engineers. The Partnership is using its best efforts to
complete SEP II in the first quarter of 1999 to coincide with the anticipated
completion of Phase I of the Terrace project. Enbridge Pipelines Inc.
("Enbridge Pipelines") (formerly Interprovincial Pipe Line Inc.) and the General
Partner are working with the Partnership's customers to develop an approach for
the initial filling of Line 14 with crude oil. Based on discussions with
customers, the line fill process will likely commence in the second quarter of
1999 following completion of line fill activities for the Terrace project. The
timing of line fill activities could impact the timing of toll increases
associated with SEP II and the Terrace Project (see " - General, - Terrace
Project"). Discussions are ongoing with the customers concerning the appropriate
timing of tariff increases for both expansion projects. The expected cost of
SEP II has increased to approximately $450 million primarily due to increased
costs of pipeline rights-of-way. The Partnership anticipates that the increased
costs will not adversely impact the Partnership or its SEP II investment due to
the tariff agreement in place with its major customers concerning SEP II.

While the Partnership believes a first quarter 1999 completion date can
be achieved, delays in project completion or increased costs might result from 
the Partnership's need to obtain a permit in Illinois from
the Board of the McHenry County Conservation District to bore underground a
planned recreation trail. The Board recently voted against granting the permit
under the proposed trail. The Partnership has filed suit in federal court
challenging this action as an infringement on interstate commerce. The
Partnership believes it will prevail in this matter; however, construction
across the recreation trail will be delayed until the matter is resolved. The
Partnership is assessing alternative approaches to resolving the issue outside 
of resolution through the courts.


Terrace Project

On April 16, 1998, the Partnership, in conjunction with affiliates Enbridge Inc.
("Enbridge"), of Calgary, Alberta (formerly IPL Energy Inc.), and Enbridge
Pipelines announced the attainment of a tariff tolling agreement ("Terrace
Agreement") with the Canadian Association of Petroleum Producers ("CAPP") with
respect to the Terrace Project. CAPP is a trade association that represents
nearly all of the Partnership's customers. The Terrace Agreement provides for a
fixed toll increase of Cdn. $0.05 per barrel for transportation from Edmonton,
Alberta to Chicago. The Cdn. $0.05 per barrel increase will be allocated between
Enbridge Pipelines and the Partnership, with the Partnership's portion added as
an incremental charge to the Partnership's SEP II tolls. The Terrace Agreement
contains provisions that may increase or decrease the Cdn. $0.05 toll increase
and may alter the allocation of the Cdn. $0.05 between Enbridge Pipelines and
the Partnership.

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<PAGE>   12

On October 27, 1998, the Partnership filed with the FERC the Terrace Agreement
and an earlier agreement signed with CAPP to cover the costs of SEP II, seeking
advance approval for the contemplated tariff surcharges for Terrace and SEP II.

Terrace is a phased expansion program that is expected to ultimately provide an
additional 520,000 barrels per day of heavy crude oil capacity for western
Canadian producers seeking greater access to Midwest U.S. markets. The first
phase of Terrace includes construction of new 36-inch diameter pipeline
facilities from Kerrobert, Saskatchewan, to Clearbrook, Minnesota, which began
in September 1998. The new pipeline will join existing 48-inch pipeline loops
between Kerrobert and Clearbrook, creating another separate pipeline joining
those locations. Subject to completion of all phases of Terrace, and after
allowing for anticipated declines in light crude oil production, total system
deliveries are expected to increase by 350,000 barrels per day.

Phase I of the Terrace Project is expected to provide an initial 95,000 barrels
per day increase in capacity in the first quarter of 1999, rising to 170,000
barrels per day by the end of 1999. The completion date of Phase I of Terrace
has been delayed approximately one month from the original anticipated date of
January 15, 1999 due to slower receipt of key construction materials. Phase I is
anticipated to cost the Partnership $138 million in the U.S., and Enbridge
Pipelines Cdn. $610 million in Canada. The Partnership expects that it will
spend approximately $100 million on its portion of Terrace in 1998 with the
remaining $38 million to be spent in 1999. Subsequent phases of Terrace are
subject to customer approval and are expected to provide the balance of the
350,000 barrels per day of added capacity.

Recent Developments

Enbridge and its affiliates are also engaged in certain North American crude oil
pipeline projects the General Partner believes are complementary to the
Partnership's expansion programs, even though the projects are not owned by the
Partnership, since these projects may result in increased deliveries on the
Partnership's pipeline system. Two of these projects in the early stages of
construction are:

-    Enbridge Pipelines (Toledo) Inc. ("Enbridge Toledo") (formerly IPL Toledo
     Pipe Line (U.S.A.) Inc.) has commenced construction of a pipeline that will
     connect the Partnership's facilities at Stockbridge, Michigan to refineries
     in Detroit, Michigan and Toledo, Ohio via 35 miles of new mainline pipe and
     53 miles of leased capacity in an existing pipeline owned by other
     companies. Construction began in May 1998 on station upgrades and in
     September 1998 on the mainline with approximately 20% having been completed
     by the end of September. Agreements have been reached with the principal
     customers regarding the level of minimum utilization for the new pipeline.
     Enbridge Toledo is expected to begin operations in the first half of 1999
     and to have an approximate capacity in excess of 80,000 barrels per day
     in heavy crude oil service.

-    Enbridge Pipelines (Athabasca) Inc. ("Enbridge Athabasca") (formerly Wild
     Rose Pipe Line Inc.) has commenced construction of a new 30-inch pipeline
     for the delivery of heavy crude oil from the Athabasca oil sands region
     near Fort McMurray, Alberta to Hardisty, Alberta. At Hardisty, Enbridge
     Athabasca will access other pipeline systems including Enbridge Pipelines'
     system in western Canada. This project will provide new pipeline capacity
     to accommodate anticipated growth in crude oil production from the
     Athabasca and Cold Lake oil sands regions. Construction of the mainline is
     approximately 45% complete with project completion targeted for April 1999.
     When fully powered, the pipeline is expected to have an ultimate capacity
     of approximately 570,000 barrels per day.

Plummer, Minnesota Incidents

On two separate occasions, Partnership pipelines in northwestern Minnesota were
damaged by a third party contractor. The first incident occurred on September
16, 1998, when approximately 5,700 barrels of crude oil were released from the
Partnership's pipeline into a farm field adjacent to the community of Plummer,
Minnesota. The Partnership's clean up and repair crews were on site within an
hour of the incident. On September 18, 1998, the pipeline repairs were
completed, the pipeline was restored to service and clean-up 

                                       10
<PAGE>   13

efforts were virtually complete. The Partnership estimates that $1.2 million
will be required to completely repair and remediate the leak site. The
Partnership anticipates that it will recover most of the repair and remediation
costs from the responsible contractor's insurance carrier or the contractor.

On October 19, 1998, a separate leak on another pipeline owned by the
Partnership resulted in the release of approximately 950 barrels of natural gas
liquids ("NGL") into the same farm field as the September 16 leak. Partnership
emergency response personnel and local emergency officials secured the leak site
and later burned the released NGL. Upon excavation of the line, it was apparent
that third-party damage was responsible for the leak. All four pipelines in the
field were excavated to ensure no further unreported third party damage exists
in the area. Costs associated with this incident are expected to approximate
$0.3 million and the General Partner will pursue recovery of all costs for the
incident from responsible parties and their insurance carriers.

Neither of these Plummer incidents are anticipated to adversely impact the
Partnership.

RECENT ACCOUNTING PRONOUNCEMENTS

On June 15, 1998, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 133, Accounting for Derivative Instruments
and Hedging Activities ("FAS 133"). FAS 133 is effective for all fiscal quarters
of all fiscal years beginning after June 15, 1999 (January 1, 2000 for the
Partnership). FAS 133 requires that all derivative instruments be recorded on
the balance sheet at their fair value. Changes in the fair value of derivatives
are recorded each period in current earnings or other comprehensive income,
depending on whether a derivative is designated as part of a hedge transaction
and, if it is the type of hedge transaction. The Partnership anticipates that,
due to its limited use of derivative instruments, the adoption of FAS 133 will
not have a significant effect on the Partnership's results of operations or its
financial position.

                                       11
<PAGE>   14
--------------------------------------------------------------------------------

PART II - OTHER INFORMATION
--------------------------------------------------------------------------------

ITEM 1.  LEGAL PROCEEDINGS
--------------------------------------------------------------------------------

On January 5, 1998, the General Partner received from the Environmental
Protection Agency ("EPA") a Request for Information pursuant to the Federal
Clean Water Act relating to a supposed discharge of oil from the Partnership's
pipeline system near Marysville, Michigan on October 4, 1994. There was no
discharge of oil from the Partnership's facility on that date but there was a
rupture of the pipeline which was undergoing a hydrostatic test and resulted in
the release of the hydrostatic test water which contained trace amounts of oil.
This incident was addressed with the Michigan Department of Natural Resources.
Cleanup of the discharged test water was completed and no civil penalty was
issued by the State of Michigan. The General Partner cooperatively responded to
the EPA's Request for Information and has received no further indications from
the EPA regarding how it intends to proceed on this matter.

In late July and early August of 1998, the Partnership's directional drilling
operations for SEP II construction caused a discharge of non-hazardous bentonite
material in a wetlands area. The Partnership reported the discharge to the U.S.
Army Corps of Engineers and the Illinois Department of Natural Resources. The
EPA issued an order suspending the drilling and requiring the Partnership to
submit a restoration and monitoring plan to assess potential long-term impact to
the site. The EPA then issued a new order which allowed the drilling to
continue. While the EPA still has the right to issue civil penalties and
injunctive relief, the Partnership does not believe that any penalties that
might later be assessed by the EPA will have a material impact on the financial
condition of the Partnership.

In a letter dated August 19, 1998, the Illinois Attorney General informed the
Partnership that it is seeking a penalty of $135,000.00 for a May 28, 1998,
release of crude oil by the Partnership in Orland Park, Illinois. The
Partnership and the Attorney General are in the process of negotiating this
matter.

The Partnership received a Notice of Violation, dated October 29, 1998, from the
Wisconsin Department of Natural Resources ("Wisconsin DNR"). The Notice alleges
that the Partnership violated the conditions of a discharge permit obtained in
connection with SEP II construction by failing to monitor discharges of water
from construction trenches on certain occasions and by exceeding the effluent
limitations set forth in the permit on certain occasions. The alleged violations
occurred during June, July and August 1998. The Partnership has submitted its
reply to the Notice and intends to cooperate with the Wisconsin DNR in an effort
to resolve the issue and any penalties that may ensue.

                                       12
<PAGE>   15
ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K
--------------------------------------------------------------------------------

a)   Exhibits

     27.1  Financial Data Schedule as of and for the nine months ended September
           30, 1998.

b)   Reports on Form 8-K

     A report on Form 8-K was filed on July 21, 1998, submitting an audited
     Consolidated Statement of Financial Position of Lakehead Pipe Line Company,
     Inc., the General Partner of Lakehead Pipe Line Partners, L.P., at December
     31, 1997 and 1996, together with the Report of Independent Public
     Accountants. A report on Form 8-K/A was filed on September 15, 1998,
     amending footnote 2 to the Consolidated Statement of Financial Position of
     Lakehead Pipe Line Company, Inc., the General Partner of Lakehead Pipe
     Line Partners, L.P. at December 31, 1997 and 1996.

                                       13
<PAGE>   16
                                    SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.




                                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                                                   (Registrant)

                           By:     Lakehead Pipe Line Company, Inc.
                                   as General Partner






                                      /s/M.A. Maki
                           ----------------------------------------------
                                         M. A. Maki
                                      Chief Accountant
                                   (Principal Financial and
                                      Accounting Officer)



                                       November 13, 1998

                                       14
<PAGE>   17
                                    SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.




                                        LAKEHEAD PIPE LINE PARTNERS, L.P.
                                                   (Registrant)

                           By:     Lakehead Pipe Line Company, Inc.
                                   as General Partner






                                    
                           ----------------------------------------------
                                         M. A. Maki
                                      Chief Accountant
                                   (Principal Financial and
                                      Accounting Officer)



                                       November 13, 1998

                                       14