<PAGE>   1
================================================================================

                                  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 MARCH 31, 1999

                                       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 333-59597

                 LAKEHEAD PIPE LINE COMPANY, LIMITED PARTNERSHIP
             (Exact name of Registrant as specified in its charter)

                DELAWARE                              39-1715851     
    (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
                                      -----   -----

================================================================================





<PAGE>   2


                                TABLE OF CONTENTS
<TABLE>
<CAPTION>
                                                                                                               PAGE
                                                                                                               ----

                          PART I. FINANCIAL INFORMATION

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

                  Statement of Income
                    for the three month periods ended March 31, 1999 and 1998..............................       1

                  Statement of Cash Flows
                    for the three month periods ended March 31, 1999 and 1998..............................       2

                  Statement of Financial Position
                    as at March 31, 1999 and December 31, 1998.............................................       3

                  Statement of Partners' Capital
                    for the three month period ended March 31, 1999........................................       4

                  Notes to Financial Statements............................................................       4

ITEM 2.         Management's Discussion and Analysis of
                  Financial Condition and Results of Operations............................................       5

ITEM 3.         Quantitative and Qualitative Disclosures About Market Risk.................................       8


<CAPTION>
                           PART II. OTHER INFORMATION

<S>             <C>                                                                                            <C>
ITEM 1.         Legal Proceedings..........................................................................       9

ITEM 6.         Exhibits and Reports on Form 8-K...........................................................      10

SIGNATURE       ...........................................................................................      11
</TABLE>


      This Quarterly Report on Form 10-Q contains forward-looking statements.
These statements are based on the Partnership's beliefs 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 identify forward-looking
statements. These statements reflect the Partnership's current views with
respect to future events and are subject to various risks, uncertainties and
assumptions including:

      -  the Partnership's dependence upon adequate supplies of and demand for
         western Canadian crude oil,

      -  the price of crude oil and the willingness of shippers to ship crude
         oil when prices are low,

      -  the Partnership's ability to complete Year 2000 readiness activities,
         and

      -  the effects of competition, in particular, by other pipeline systems. 

If one or more of these risks or uncertainties materialize, or should underlying
assumptions prove incorrect, actual results may vary materially from those
described in this Form 10-Q. Except as required by applicable securities laws,
the Partnership does not intend to update these forward-looking statements. For
additional discussion of such risks, uncertainties and assumptions, see the
Partnership's 1998 Annual Report on Form 10-K.



<PAGE>   3


--------------------------------------------------------------------------------
PART I - FINANCIAL INFORMATION
--------------------------------------------------------------------------------

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


                 LAKEHEAD PIPE LINE COMPANY, LIMITED PARTNERSHIP
                               STATEMENT OF INCOME

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

                                                                                                THREE MONTHS ENDED
                                                                                                    MARCH 31,
(UNAUDITED; DOLLARS IN MILLIONS)                                                              1999            1998
-------------------------------------------------------------------------------------------------------------------


<S>                                                                                       <C>             <C>  
Operating Revenue                                                                         $    74.0       $    72.9
-------------------------------------------------------------------------------------------------------------------


Expenses
   Power                                                                                       13.5            17.7
   Operating and administrative                                                                13.8            16.8
   Depreciation (Note 3)                                                                       13.5            10.4
-------------------------------------------------------------------------------------------------------------------

                                                                                               40.8            44.9
-------------------------------------------------------------------------------------------------------------------


Operating Income                                                                               33.2            28.0

Interest and Other Income                                                                       1.5             2.9

Interest Expense                                                                              (12.7)           (7.7)
-------------------------------------------------------------------------------------------------------------------


Net Income                                                                                $    22.0       $    23.2
===================================================================================================================
</TABLE>


See accompanying notes to the financial statements.


                                       1


<PAGE>   4


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

                 LAKEHEAD PIPE LINE COMPANY, LIMITED PARTNERSHIP
                             STATEMENT OF CASH FLOWS

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

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

                                                                                                THREE MONTHS ENDED
                                                                                                     MARCH 31,
(UNAUDITED; DOLLARS IN MILLIONS)                                                                 1999         1998
-------------------------------------------------------------------------------------------------------------------


<S>                                                                                          <C>          <C>   
Cash Provided from Operating Activities
   Net income                                                                                $   22.0     $   23.2
   Adjustments to reconcile net income to
     cash provided from operating activities:
        Depreciation                                                                             13.5         10.4
        Interest on accrued rate refunds (Note 4)                                                 0.3          0.7
        Other                                                                                     0.4          0.1
        Changes in operating assets and liabilities:
           Accounts receivable and other                                                         (2.7)         4.8
           Materials and supplies                                                                (0.1)        (0.1)
           General Partner and affiliates                                                        (5.3)        (3.8)
           Accounts payable and other                                                            (4.0)         3.5
           Interest payable                                                                      10.5          7.2
           Property and other taxes                                                               2.1          3.0
           Payment of rate refunds and related interest (Note 4)                                 (7.3)        (7.2)
-------------------------------------------------------------------------------------------------------------------


                                                                                                 29.4         41.8
-------------------------------------------------------------------------------------------------------------------


Investing Activities
   Additions to property, plant and equipment                                                   (17.3)       (81.8)
   Short-term investments, net                                                                    -           36.4
   Advances to affiliate                                                                          -           (6.9)
   Changes in construction payables                                                             (34.8)        (3.1)
-------------------------------------------------------------------------------------------------------------------

                                                                                                (52.1)       (55.4)
-------------------------------------------------------------------------------------------------------------------


Financing Activities
   Variable rate financing, net                                                                  20.0          -
   Loan from General Partner                                                                     25.0          -
   Distributions to partners                                                                    (24.8)       (22.0)
-------------------------------------------------------------------------------------------------------------------


                                                                                                 20.2        (22.0)
-------------------------------------------------------------------------------------------------------------------


Decrease in Cash and Cash Equivalents *                                                          (2.5)       (35.6)

Cash and Cash Equivalents at Beginning of Period                                                 47.0        118.6
-------------------------------------------------------------------------------------------------------------------

Cash and Cash Equivalents at End of Period                                                   $   44.5     $   83.0
===================================================================================================================
</TABLE>


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

See accompanying notes to the financial statements.


                                       2
<PAGE>   5


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

                 LAKEHEAD PIPE LINE COMPANY, LIMITED PARTNERSHIP
                         STATEMENT OF FINANCIAL POSITION

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

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


                                                                                      MARCH 31,       DECEMBER 31,
(UNAUDITED, EXCEPT FOR DECEMBER 31, 1998; DOLLARS IN MILLIONS)                             1999               1998
---------------------------------------------------------------------------------------------------------------------


                                     ASSETS
<S>                                                                                   <C>              <C>
Current Assets
   Cash and cash equivalents                                                          $    44.5           $    47.0
   Due from General Partner and affiliates                                                  2.4                  -
   Advances to affiliate                                                                   32.0                32.0
   Accounts receivable and other                                                           27.9                25.2
   Materials and supplies                                                                   7.2                 7.1
---------------------------------------------------------------------------------------------------------------------


                                                                                          114.0               111.3
---------------------------------------------------------------------------------------------------------------------


Deferred Charges and Other                                                                  6.5                 6.9
---------------------------------------------------------------------------------------------------------------------


Property, Plant and Equipment
   At cost                                                                              1,504.3             1,487.3
   Accumulated depreciation                                                              (204.3)             (191.1)
---------------------------------------------------------------------------------------------------------------------


                                                                                        1,300.0             1,296.2
---------------------------------------------------------------------------------------------------------------------


                                                                                      $ 1,420.5           $ 1,414.4
=====================================================================================================================



<CAPTION>
                        LIABILITIES AND PARTNERS' CAPITAL
<S>                                                                                   <C>              <C>
Current Liabilities
   Due to General Partner and affiliates                                              $     -             $     2.9
   Accounts payable and other                                                              14.5                53.3
   Interest payable                                                                        16.0                 5.5
   Property and other taxes                                                                14.0                11.9
   Accrued rate refunds and related interest (Note 4)                                      21.7                28.7
---------------------------------------------------------------------------------------------------------------------


                                                                                           66.2               102.3

Long-Term Debt                                                                            834.5               814.5
Loan from General Partner                                                                  25.0                 -
Contingencies (Note 5)
---------------------------------------------------------------------------------------------------------------------


                                                                                          925.7               916.8
---------------------------------------------------------------------------------------------------------------------


Partners' Capital (Note 6)
   Limited Partner                                                                        492.2               495.0
   General Partner                                                                          2.6                 2.6
---------------------------------------------------------------------------------------------------------------------


                                                                                          494.8               497.6
---------------------------------------------------------------------------------------------------------------------


                                                                                      $ 1,420.5           $ 1,414.4
=====================================================================================================================
</TABLE>


See accompanying notes to the financial statements.


                                       3
<PAGE>   6


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

                 LAKEHEAD PIPE LINE COMPANY, LIMITED PARTNERSHIP
                         STATEMENT OF PARTNERS' CAPITAL

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

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

(UNAUDITED, EXCEPT FOR DECEMBER 31, 1998;                                  LIMITED        GENERAL
 DOLLARS IN MILLIONS)                                                      PARTNER        PARTNER            TOTAL
---------------------------------------------------------------------------------------------------------------------


<S>                                                                      <C>              <C>              <C>      
Partners' Capital at December 31, 1998                                   $   495.0         $   2.6         $   497.6

Net Income Allocation                                                         21.7             0.3              22.0

Distributions to Partners                                                    (24.5)           (0.3)            (24.8)

---------------------------------------------------------------------------------------------------------------------
Partners' Capital at March 31, 1999                                      $   492.2         $   2.6         $   494.8

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



See accompanying notes to the financial statements.



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

                  NOTES TO THE FINANCIAL STATEMENTS (UNAUDITED)

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

1.   Basis of Presentation

     The accompanying unaudited 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 March 31, 1999 and December 31,
     1998; the results of operations for the three month periods ended March 31,
     1999 and 1998; and cash flows for the three month periods ended March 31,
     1999 and 1998. The results of operations for the three months ended March
     31, 1999 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 financial statements and notes thereto
     presented in the Partnership's 1998 Annual Report on Form 10-K.

2.   Comparative Amounts

     Certain comparative amounts are reclassified to conform with the current
     quarter's financial statement presentation.

3.   Depreciation Rates

     Revised depreciation rates were filed with the Federal Energy Regulatory
     Commission ("FERC") to be effective on January 1, 1999, better representing
     the expected remaining service life of the pipeline system and coinciding
     with the in-service date for the System Expansion Program II ("SEP II").
     Depreciation expense for the three-months ended March 31, 1999, is $1.6
     million lower than it would have been under previous depreciation rates.

4.   Accrued Rate Refunds and Related Interest

     In 1996, FERC approved a settlement agreement ("Settlement Agreement")
     between the Partnership and 


                                       4
<PAGE>   7

     customer representatives on all 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 $21.7 million total rate refund
     balance remaining at March 31, 1999 is being repaid through a 10% reduction
     in tariff rates. This reduction will continue until all refunds have been
     made, which is expected to occur during the fourth quarter of 1999.
     Interest will continue to accrue on the unpaid balance based on the 90-day
     Treasury bill rate.

5.   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 covered 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.

6.   Partners' Capital Contribution

     On April 28, 1999, the Partnership received net partner contributions of
     approximately $121.0 million. These proceeds were used to repay
     indebtedness incurred under the Partnership's Revolving Credit Facility.


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


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

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

RESULTS OF OPERATIONS

Net income for the first quarter of 1999 was $22.0 million, compared with 1998
first quarter net income of $23.2 million, a decrease of $1.2 million. The
decrease in net income was primarily due to higher interest expense, partially
offset by lower operating expenses.

Operating revenue for the first quarter of 1999 was approximately the same as
first quarter 1998 as a decline in deliveries was largely offset by increased
tariffs effective January 1, 1999. Deliveries averaged 1,394,000 barrels per day
for the first quarter of 1999, down 12% from the 1,588,000 averaged for the
first quarter of last year. This decrease stems primarily from low crude oil
prices since mid-1998, which reduced the supply of crude oil available to the
Partnership. First quarter deliveries were also adversely impacted by the
process of filling new lines with crude oil and by maintenance activities at a
number of refinery sites. The Partnership expects that average daily deliveries
for 1999 will be approximately 1.5 million barrels per day, which is consistent
with the estimate made in December 1998. System utilization, measured in barrel
miles, was 89 billion for the first quarter of 1999, as compared to 99 billion
for last year's first quarter, reflecting decreased deliveries by the
Partnership.

Total operating expenses for the first quarter of 1999 decreased $4.1 million,
or 9.1%, from the corresponding period of 1998. The decline resulted from lower
power costs associated with reduced deliveries and lower operating and
administrative costs due to cost control efforts by the Partnership and timing
of maintenance activities. These savings were partially offset by increased
depreciation expense resulting from the placing in service of SEP II. The
depreciation expense increase was somewhat offset by 


                                       5
<PAGE>   8

revised depreciation rates filed with FERC to be effective on January 1, 1999,
to better represent the expected remaining service life of the pipeline system
and to coincide with the in-service date for SEP II. Depreciation expense for
the three-months ended March 31, 1999, is $1.6 million lower than it would have
been under previous depreciation rates.

Interest and other income for the first three months of 1999 was $1.4 million
less than the same period in 1998 primarily due to lower interest income from
lower cash balances as a result of SEP II and Terrace (see " General, - Terrace
Program") capital expenditures. Interest expense increased $5.0 million due to
higher borrowings associated with the Partnership's expansion projects.

LIQUIDITY AND CAPITAL RESOURCES

The Partnership anticipates that it will continue to have adequate liquidity to
fund future recurring operating, investing and financing activities. The
Partnership intends to fund the remaining portion of Terrace (see " General, -
Terrace Program") and ongoing capital expenditures with the proceeds from future
partner capital contributions, debt offerings, borrowings, cash generated from
operating activities, and existing cash and cash equivalents. Cash distributions
are expected to be funded with internally generated cash. The Partnership's
ability to make future debt offerings and receive partner capital contributions
will depend on prevailing market conditions and interest rates and the
then-existing financial condition of the Partnership.

At March 31, 1999, cash and cash equivalents totaled $44.5 million, as compared
to $47.0 million at December 31, 1998, as cash required for distributions and
capital expenditures slightly exceeded cash generated from operating activities
and borrowings under the Partnership's Revolving Credit Facility and from the
General Partner. Of this $44.5 million, $25.3 million will be used for the cash
distribution payable May 15, 1999, with the remaining $19.2 million available
for capital expenditures or other business needs.

Due to changes in working capital, cash flow from operating activities for the
first quarter of 1999 was $29.4 million, as compared with $41.8 million for the
same period last year.

In late March 1999, the Partnership borrowed $25 million from the General
Partner under an arrangement pursuant to which the General Partner is authorized
to make loans from time to time to the Partnership, on an uncommitted basis, in
an amount not to exceed $200 million. Interest on the loan accrued at a rate of
7.75%. This loan was repaid in early April.

On April 28, 1999, the Partnership received net partner contributions of
approximately $121.0 million. These proceeds were used to repay indebtedness
incurred under the Partnership's Revolving Credit Facility.

Capital expenditures for the first quarter of 1999 totaled $17.3 million, of
which $14.0 million was for the first phase of the Terrace program (see " -
General, - Terrace Program"). The first phase of the Terrace program is largely
complete with $126.7 million of the anticipated $138.0 million total capital
expenditures incurred through March 31, 1999. In addition to Terrace, the
Partnership anticipates spending approximately $8.2 million for pipeline system
enhancements and $13.5 million for core maintenance activities in 1999.
Additional capital expenditures for SEP II will be incurred for minor
restoration and clean-up work and finalization of rights-of-way costs. It is not
anticipated that these expenditures will be material in comparison to the $450
million cost of the project.

GENERAL

Year 2000 Issue
---------------

The Year 2000 Readiness Program, which is being undertaken jointly by the
Partnership and its Enbridge affiliates, continued on schedule, having attained
several milestone points by March 31, 1999. Remediation, testing and deployment
of critical systems that control the flow of crude oil and natural gas liquids
in the Partnership's pipeline system are on target for completion by June 30,
1999.


                                       6
<PAGE>   9

In order to address unforeseen year 2000 problems that could arise and in an
attempt to minimize business disruptions, the Partnership is developing business
continuity plans for all critical processes, systems, technologies and external
relationships. These plans are expected to be completed by mid 1999. As part of
the continuity planning process, significant external relationships are being
investigated. The most significant of these relationships are reliance on
electrical and telecommunication suppliers as well as connecting pipelines and
refineries.

For additional discussion of the year 2000 issue, see the Partnership's 1998
Annual Report on Form 10-K.

Terrace Program
---------------

The Terrace program, which is being undertaken by the Partnership in conjunction
with Enbridge Pipelines Inc. ("Enbridge Pipelines"), the parent company of the
General Partner, is a multi-phased expansion program. Subject to continued
industry support, customer requirements and receipt of regulatory approvals,
this multi-phased expansion program is expected to be completed over the period
1999 through 2005.

Phase I of the Terrace expansion program 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. Phase I of the Terrace Program will
be completed in two stages during 1999 and is expected to provide 170,000
barrels per day of added heavy crude oil capacity from the Canadian border to
Superior, Wisconsin by September 1999. Of this additional capacity,
approximately 95,000 barrels per day should be available during the second
quarter of this year. Phase I is anticipated to cost the Partnership $138
million in the U.S., and to cost Enbridge Pipelines Cdn. $610 million in Canada.
The Partnership expects that it will spend approximately $25.3 million on its
portion of Terrace during 1999.

Subsequent to the completion of all phases of Terrace, and after allowing for
anticipated declines in light crude oil production, total system delivery
capability is expected to increase by approximately 350,000 barrels per day.

Tariff Matters
--------------

The Partnership filed a tariff agreement ("Tariff Agreement") with FERC
providing for tariff rate surcharges commencing as of January 1, 1999 (with
respect to SEP II) and April 1, 1999 (with respect to Terrace). This filing
consolidated the Partnership's 1996 settlement agreement ("Settlement
Agreement") with respect to SEP II and other significant agreements with
customers concerning Terrace and the transportation of heavy crude oil. FERC
approved the Tariff Agreement, which allows the Partnership to earn a return on
its SEP II equity investment that varies with utilization of SEP II capacity on
Enbridge Pipelines' system. Under the Tariff Agreement, return on SEP II equity
can range from a minimum of 7.5% to a maximum of 15%.

Under the Tariff Agreement, the tariff rate surcharge for SEP II is
approximately $0.11 per barrel for light crude oil to Chicago, Illinois. This
surcharge allows the Partnership to recover the cost of service for SEP II
facilities and earn a 7.5% return on SEP II equity investment during 1999.

The tariff rate surcharge for Terrace is approximately $0.013 per barrel for
light crude oil to Chicago. This tariff surcharge is based upon the assumption
that Phases II and III of Terrace will be completed. If these phases of Terrace
are not completed, the Tariff Agreement provides that the Partnership will be
allowed to increase the tariff surcharge on a cost of service basis to allow
recovery of, and return on, the Partnership's Phase I Terrace investment
including any revenue variances between the application of the toll increment
and the annual cost of service of Terrace.

Other Developments
------------------


                                       7
<PAGE>   10

Enbridge and its affiliates have also recently completed additional North
American crude oil pipeline projects. The Partnership believes that these
projects, even though they are not owned by the Partnership, are complementary
to and may result in increased deliveries on the Partnership's pipeline system.
Two of these projects are:

-    Enbridge Toledo - Enbridge has completed construction of a new pipeline
     that connects the Partnership's facilities at Stockbridge, Michigan to two
     refineries in the Toledo, Ohio area. This pipeline is anticipated to have
     capacity in excess of 80,000 barrels per day in heavy crude oil service and
     became available for service in early February 1999.

-    Enbridge Athabasca - In March 1999, Enbridge completed construction of a
     new 30-inch diameter pipeline for the delivery of heavy crude oil from the
     Athabasca oil sands region near Fort McMurray, Alberta to Hardisty,
     Alberta. At Hardisty, the Athabasca pipeline accesses other pipeline
     systems including Enbridge Pipelines' system in western Canada. This
     project provides new pipeline capacity to accommodate anticipated growth in
     crude oil production from the Athabasca oil sands region. When fully
     powered, the Athabasca pipeline is anticipated to have an ultimate capacity
     of approximately 570,000 barrels per day. Enbridge has entered into a
     30-year transportation arrangement with Suncor Energy Inc., the initial
     shipper on the pipeline.


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


ITEM 3.       QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET RISK

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

The Partnership's market risk is primarily impacted by changes in interest
rates. The Partnership has minimal foreign exchange risk and its cash flows are
not significantly impacted by changes in commodity prices, as the Partnership
does not own the crude oil and NGL it transports. However, commodity prices have
a significant impact on the underlying supply and demand for crude oil and NGL
that the Partnership transports. The Partnership does not currently hold or
issue derivative instruments for trading or any other purposes.

The Partnership's market risk with respect to interest rate exposure is managed
through its long-term debt ratio target, and its allocation of fixed and
floating rate debt. Information about the Partnership's financial instruments
that are sensitive to changes in interest rates has not changed from that
presented in the Partnership's 1998 Annual Report on Form 10-K.













                                       8

<PAGE>   11



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


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


In late July 1998, the Partnership's directional drilling operations for SEP II
construction caused a discharge of non-hazardous bentonite drilling mud in a
wetlands area. The State of Illinois is pursuing an action relating to this
discharge under Natural Resource Damage Assessment regulations of the Clean
Water Act to seek compensation for damage to the wetlands area. It is expected
that a settlement will be reached with the State to resolve the matter and that
it will not have a material impact on the financial condition of the
Partnership. The U.S. Environmental Protection Agency ("EPA") issued an
information request on April 6, 1999, seeking information regarding the
selection of the pipeline route through the wetlands area. The Partnership
responded to the information request on April 20, 1999. The EPA has also
informed the Partnership that it is preparing to file an administrative
complaint in the next several weeks seeking a civil administrative penalty for
violations of the Clean Water Act resulting from the bentonite discharges into
the wetlands.

The Illinois Attorney General is seeking payment of a penalty of $98,000 and
costs of $2,000 for a May 28, 1998, release of crude oil caused by a third party
in Orland Park, Illinois. The Partnership and the Attorney General are
negotiating the terms of a Consent Order to be entered by the Attorney General
with the concurrence of the Partnership, the General Partner, and the third
party.

The Partnership received a Notice of Violation, dated October 29, 1998, from the
Wisconsin Department of Natural Resources ("Wisconsin DNR") that alleges the
Partnership failed to monitor discharges of water from SEP II construction
trenches on certain occasions and exceeded the effluent limitations set forth in
a permit. 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. It is not anticipated that any penalty will have a
material impact on the financial condition of the Partnership.













                                       9
<PAGE>   12



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


ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

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

<S>  <C>       <C>
a)   Exhibits

     27.1      Financial Data Schedule as of and for the three months ended 
               March 31, 1999.

b)   Reports on Form 8-K

     No reports on Form 8-K were filed during the quarter ended March 31, 1999.
</TABLE>










                                       10
<PAGE>   13




                                    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 COMPANY, LIMITED PARTNERSHIP
                                                   (Registrant)

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



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



                                     Dated:  May 14, 1999






                                       11