<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 JUNE 30, 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
                                                                          PAGE
                         PART I - FINANCIAL INFORMATION                   ----

ITEM 1.  Financial Statements

           Statement of Income for the three month
             and six month periods ended June 30, 1999 and 1998..........   1

           Statement of Cash Flows
             for the six month periods ended June 30, 1999 and 1998......   2

           Statement of Financial Position
             as at June 30, 1999 and December 31, 1998...................   3

           Statement of Partners' Capital
             for the six month period ended June 30, 1999................   4

           Notes to the 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......   9


                           PART II - OTHER INFORMATION

ITEM 1.  Legal Proceedings...............................................  11

ITEM 6.  Exhibits and Reports on Form 8-K................................  12

SIGNATURE  ..............................................................  13


      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 these 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        Six months ended
                                                                            June 30,                 June 30,
(unaudited; dollars in millions)                                       1999     1998            1999         1998
---------------------------------------------------------------------------------------------------------------------
<S>                                                                 <C>           <C>         <C>           <C>
Operating Revenue                                                   $  80.4       $  74.4     $  154.4      $  147.3
---------------------------------------------------------------------------------------------------------------------
Expenses
   Power                                                               13.6          18.9         27.1          36.6
   Operating and administrative                                        16.8          16.5         30.6          33.3
   Depreciation (Note 3)                                               14.6          10.4         28.1          20.8
---------------------------------------------------------------------------------------------------------------------
                                                                       45.0          45.8         85.8          90.7
---------------------------------------------------------------------------------------------------------------------
Operating Income                                                       35.4          28.6         68.6          56.6

Interest and Other Income                                               0.7           1.1          2.2           4.0

Interest Expense                                                      (13.4)         (5.3)       (26.1)        (13.0)
---------------------------------------------------------------------------------------------------------------------
Net Income                                                          $  22.7       $  24.4     $   44.7      $   47.6
=====================================================================================================================
</TABLE>



See accompanying notes to the financial statements.


                                       1

<PAGE>   4

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

                 LAKEHEAD PIPE LINE COMPANY, LIMITED PARTNERSHIP
                             STATEMENT OF CASH FLOWS
--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                                   Six months ended
                                                                                        June 30,
(unaudited; dollars in millions)                                                   1999         1998
--------------------------------------------------------------------------------------------------------
<S>                                                                            <C>             <C>
Cash Provided from Operating Activities
   Net income                                                                   $   44.7        $   47.6
   Adjustments to reconcile net income to
     cash provided from operating activities:
        Depreciation                                                                28.1            20.8
        Interest on accrued rate refunds (Note 4)                                    0.5             1.3
        Other                                                                       (0.6)            0.1
        Changes in operating assets and liabilities:
           Accounts receivable and other                                            (0.7)            5.2
           Materials and supplies                                                   (0.5)           (0.2)
           General Partner and affiliates                                           (4.2)           (3.7)
           Accounts payable and other                                               (4.8)            4.0
           Interest payable                                                         (0.1)           (1.3)
           Property and other taxes                                                 (2.5)           (2.8)
           Payment of rate refunds and related interest (Note 4)                   (15.2)          (14.6)
--------------------------------------------------------------------------------------------------------
                                                                                    44.7            56.4
--------------------------------------------------------------------------------------------------------
Investing Activities
   Short-term investments, net                                                      --              41.3
   Repayments from (advances to) affiliate                                           3.9            (6.8)
   Additions to property, plant and equipment                                      (42.8)         (223.9)
   Changes in construction payables                                                (26.0)           (3.2)
--------------------------------------------------------------------------------------------------------
                                                                                   (64.9)         (192.6)
--------------------------------------------------------------------------------------------------------
Financing Activities
   Variable rate financing, net                                                    (55.0)          107.0
   Partners' capital contributions, net (Note 5)                                   120.9            --
   Distributions to partners                                                       (52.6)          (46.7)
   Other                                                                            --              (0.2)
--------------------------------------------------------------------------------------------------------
                                                                                    13.3            60.1
--------------------------------------------------------------------------------------------------------
Decrease in Cash and Cash Equivalents *                                             (6.9)          (76.1)

Cash and Cash Equivalents at Beginning of Period                                    47.0           118.6
--------------------------------------------------------------------------------------------------------
Cash and Cash Equivalents at End of Period                                      $   40.1        $   42.5
========================================================================================================
</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>
                                                                                    June 30,      December 31,
(unaudited, except for December 31, 1998; dollars in millions)                          1999              1998
--------------------------------------------------------------------------------------------------------------
                                     ASSETS
<S>                                                                              <C>             <C>
Current Assets
   Cash and cash equivalents                                                      $     40.1      $     47.0
   Due from General Partner and affiliates                                               1.3            --
   Advances to affiliate                                                                28.1            32.0
   Accounts receivable and other                                                        25.9            25.2
   Materials and supplies                                                                7.6             7.1
--------------------------------------------------------------------------------------------------------------
                                                                                       103.0           111.3
--------------------------------------------------------------------------------------------------------------
Deferred Charges and Other                                                               7.3             6.7
--------------------------------------------------------------------------------------------------------------
Property, Plant and Equipment
   At cost                                                                           1,529.2         1,487.3
   Accumulated depreciation                                                           (218.3)         (191.1)
--------------------------------------------------------------------------------------------------------------
                                                                                     1,310.9         1,296.2
--------------------------------------------------------------------------------------------------------------
                                                                                  $  1,421.2      $  1,414.2
==============================================================================================================
</TABLE>

<TABLE>
<CAPTION>

                        LIABILITIES AND PARTNERS' CAPITAL
<S>                                                                              <C>             <C>
Current Liabilities
   Due to General Partner and affiliates                                          $     --        $      2.9
   Accounts payable and other                                                           22.5            53.3
   Interest payable                                                                      5.4             5.5
   Property and other taxes                                                              9.4            11.9
   Accrued rate refunds and related interest (Note 4)                                   14.0            28.7
---------------------------------------------------------------------------------------------------------------
                                                                                        51.3           102.3

Long-Term Debt                                                                         759.5           814.5
Contingencies (Note 6)
---------------------------------------------------------------------------------------------------------------
                                                                                       810.8           916.8
---------------------------------------------------------------------------------------------------------------
Partners' Capital
   Limited Partner                                                                     606.6           494.8
   General Partner                                                                       3.8             2.6
---------------------------------------------------------------------------------------------------------------
                                                                                       610.4           497.4
---------------------------------------------------------------------------------------------------------------
                                                                                  $  1,421.2      $  1,414.2
===============================================================================================================
</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                                   $  494.8          $  2.6        $  497.4

Partners' Capital Contributions, net (Note 5)                               119.7             1.2           120.9

Net Income Allocation                                                        44.2             0.5            44.7

Distributions to Partners                                                   (52.1)           (0.5)          (52.6)
-------------------------------------------------------------------------------------------------------------------
Partners' Capital at June 30, 1999                                       $  606.6          $  3.8        $  610.4
===================================================================================================================
</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 June 30, 1999 and December 31,
     1998; the results of operations for the three and six month periods ended
     June 30, 1999 and 1998; and cash flows for the six month periods ended June
     30, 1999 and 1998. The results of operations for the six months ended June
     30, 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
     period's financial statement presentation.

3.   Depreciation Rates

     Revised depreciation rates were approved by 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 month and six month periods ended June
     30, 1999, is $1.8 million and $3.4 million lower, respectively, 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



                                       4
<PAGE>   7

     and 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 $14.0 million total rate refund
     balance remaining at June 30, 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.   Partners' Capital Contributions

     On April 28, 1999, the Partnership received capital contributions from its
     Partners providing net proceeds of $120.9 million. The proceeds were used
     to repay indebtedness under the Partnership's Revolving Credit Facility
     incurred to finance pipeline expansion projects.

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 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.

7.   Subsequent Event

     On July 15, 1999, the Partnership entered into an interest rate swap
     agreement with a notional amount of $50.0 million to hedge its variable
     rate indebtedness under the Partnership's Revolving Credit Facility. Under
     the three-year agreement, the Partnership makes or receives quarterly
     payments based on a fixed rate of 6.231%.


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

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

RESULTS OF OPERATIONS

SIX MONTHS ENDED JUNE 30, 1999 COMPARED WITH SIX MONTHS ENDED JUNE 30, 1998

Net income for the six months ended June 30, 1999, was $44.7 million, compared
to $47.6 million, for the same period in 1998. The decline in net income for the
first half reflects higher interest expense and lower interest income, which
were partially offset by higher operating revenue and lower operating expenses.

Operating revenue for the first six months of 1999 increased $7.1 million, to
$154.4 million, over the corresponding period in 1998 as declines in deliveries
were more than offset by increased tariffs (see "General, - Tariff Matters").
Deliveries averaged 1.386 million barrels per day for the first six months of



                                       5
<PAGE>   8

1999, compared to 1.598 million barrels per day for the same period of 1998. The
reduction stems primarily from low crude oil prices in 1998 and early 1999 that
continue to impact the supply of crude oil available to the Partnership. System
utilization, measured in barrel miles, was 176 billion for the first six months
of 1999, compared to 200 billion for the first half of last year, reflecting the
decline in deliveries. With the recent emergence from the low crude oil price
environment, continued strength and stability of oil prices are expected to
result in modest growth in deliveries over the near term as western Canadian
production returns to previous levels.

Total operating expenses for the first six months of 1999 decreased $4.9 million
from the corresponding period last year. The decline resulted from lower power
and operating and administrative costs offset by higher depreciation costs.
Power costs decreased $9.5 million due to lower deliveries. Operating and
administrative costs decreased $2.7 million primarily due to timing and cost
control efforts by the Partnership. Depreciation expense increased $7.3 million
primarily due to placing SEP II in service January 1, 1999, which was partially
offset by reduced depreciation rates.

Interest expense for the first six months of 1999 was $13.1 million higher than
the same period of 1998 due to higher borrowings associated with the
Partnership's expansion projects.

THREE MONTHS ENDED JUNE 30, 1999 COMPARED WITH THREE MONTHS ENDED JUNE 30, 1998

Net income for the three months ended June 30, 1999, was $22.7 million, compared
to $24.4 million, for the same period last year. The decline in quarterly
results reflects higher interest expense, which was partially offset by higher
operating revenue.

Operating revenue for the second quarter of 1999 was $80.4 million, an increase
of $6.0 million over the corresponding period in 1998, as declines in deliveries
were more than offset by increased tariffs. Deliveries averaged 1.377 million
barrels per day for the second quarter of 1999, compared to 1.608 million
barrels per day for the same period of 1998. As previously noted, the reduction
stems primarily from low crude oil prices in 1998 and early 1999 that continue
to impact the supply of crude oil available to the Partnership. Second quarter
1999 deliveries were also affected by scheduled and unscheduled maintenance
activities at a number of refinery sites served by the Partnership. System
utilization, measured in barrel miles, was 87 billion for the second quarter of
1999 compared to 101 billion for the same period in 1998, reflecting the decline
in deliveries.

Total operating expenses for the three months ended June 30, 1999, decreased
slightly by $0.8 million from the corresponding period in 1998. Decreased power
costs of $5.3 million were largely offset by higher depreciation costs of $4.2
million. Power costs decreased due to lower deliveries. Depreciation expense
increased due to placing SEP II in service January 1, 1999, which was partially
offset by reduced depreciation rates.

As previously noted, interest expense for the second quarter of 1999 was $8.1
million higher than the same period of 1998 due to higher borrowings associated
with the Partnership's expansion projects.

The results of operations for the three month and six month periods ended June
30, 1999 should not be taken as indicative of the results of operations expected
for the full year.

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


                                       6
<PAGE>   9

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 June 30, 1999, cash and cash equivalents totaled $40.1 million, as compared
to $47.0 million at December 31, 1998, as cash required for distributions,
repayments of variable rate financing and capital related expenditures exceeded
cash generated from operating activities and net proceeds from partner capital
contributions. Of this $40.1 million, $27.9 million will be used for the cash
distribution payable August 13, 1999, with the remaining $12.2 million available
for capital expenditures or other business needs.

Due to increased working capital requirements, cash flow from operating
activities for the first six months of 1999 was $44.7 million, as compared with
$56.4 million for the same period last year.

On April 28, 1999, the Partnership received net partner capital contributions of
$120.9 million. These proceeds were used to repay indebtedness under the
Partnership's Revolving Credit Facility, incurred to finance pipeline expansion
projects.

Capital expenditures for the first half of 1999 totalled $42.8 million, of which
$18.2 million was for the first phase of the Terrace program (see " - General,
Terrace Program"). The first phase of the Terrace program is substantially
complete with $130.9 million of the Partnership's anticipated $138.0 million
total capital expenditures incurred through June 30, 1999. In addition to
Terrace, the Partnership anticipates capital expenditures of $51.6 million in
1999 including $7.7 million for pipeline system enhancements, $13.7 million for
core maintenance activities and additional capital expenditures related to SEP
II that 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 $450.0 million cost of the
SEP II project.

GENERAL

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 of both the United States
and Canadian portions of the pipeline system. 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 is being 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. The first stage of Phase I was
substantially completed in the first quarter of 1999 and the second stage is
expected to be completed in October 1999. Phase I is expected to cost the
Partnership approximately $138.0 million for construction of facilities in the
United States, and to cost Enbridge Pipelines approximately Cdn. $610.0 million
for construction of facilities in Canada. Through June 30, 1999, the Partnership
spent $130.9 million for construction of Phase I facilities in the United
States.

Subsequent phases of Terrace will depend on customer requirements and, if
completed, are expected to provide up to 350,000 barrels per day of heavy crude
oil capacity in addition to the 170,000 barrels per


                                       7
<PAGE>   10

day to be provided by Phase I. Subject to 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.

Other Developments

Enbridge Inc. ("Enbridge"), the ultimate parent company of the General Partner,
and its affiliates have 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 will result in
increased deliveries on the Partnership's pipeline system. These projects
include:

     -   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 has a capacity
         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 synthetic 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' portion
         of the system in western Canada. This project provides new pipeline
         capacity to accommodate anticipated growth in crude oil production in
         the Athabasca oil sands region. 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.

Montreal Extension Reversal

The Enbridge Pipelines' system includes a section that extends from Sarnia,
Ontario, to Montreal, Quebec ("Line 9"), which at one time flowed in a
west-to-east direction. Enbridge Pipelines and a group of refiners developed the
Line 9 reversal project which enables crude oil to be imported into eastern
Canada through the facilities of Portland Pipe Line Corporation and Montreal
Pipe Line Limited. During the second quarter of 1999, Line 9 began operations in
an east-to-west direction from Montreal to the major refining centers in
Ontario. Line 9 is being reversed in two stages. The first stage entered service
in the second quarter of 1999 with a capacity of 120,000 barrels per day from
Montreal to North Westover, Ontario. Construction to allow for full reversal is
expected to be completed late in the third quarter or early in the fourth
quarter of 1999 at a capacity of 240,000 barrels per day from Montreal to
Sarnia. The reversal of Line 9 has resulted in Enbridge Pipelines becoming a
competitor of the Partnership's system for supplying crude oil to the Ontario
market. This reversal is expressly permitted by the agreements entered into at
the time of formation of the Partnership.

The reversal of Line 9 has resulted in decreased deliveries over the
Partnership's system to eastern Canada during the second quarter. The
Partnership anticipates that displaced volumes originating in western Canada
will be diverted to other markets in the Midwest U.S. The Partnership
anticipates that U.S. domestic and foreign crude oil volumes that enter the
Partnership's system in Chicago for delivery to eastern Canada will also decline
from recent historical levels due to the reversal of Line 9. For additional
information on the Line 9 reversal please refer to the Partnership's 1998 Annual
Report on Form 10-K. The level of decline in deliveries over the Partnership's
system to eastern Canada will be dependent upon global crude oil market dynamics
and the level of utilization of Line 9.


                                       8
<PAGE>   11


Tariff Matters

The Partnership filed a tariff agreement ("Tariff Agreement") with FERC
providing for tariff rate surcharges commencing as of January 1, 1999 for SEP II
and April 1, 1999 for Terrace. This filing consolidated the Partnership's 1996
settlement agreement ("Settlement Agreement") for SEP II and other significant
agreements with customers concerning Terrace and the transportation of heavy
crude oil. The 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' portion of the system. Under the Tariff
Agreement, the return on SEP II equity can range from a minimum of 7.5% to a
maximum of 15%. For 1999, 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 assumes completion of Phases
II and III of Terrace. 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.

Effective July 1, 1999, in compliance with the indexed rate ceilings allowed by
FERC, the Partnership decreased its rates for transportation approximately 1.8%.
The decrease in tariff rates is not expected to have a significant impact on the
Partnership.

Year 2000

The Partnership's pipeline system is operationally dependent on the ability of
Enbridge Pipelines to transport crude oil and other liquid hydrocarbons from
western Canada to reach markets in the United States and eastern Canada. Due to
the integrated nature of these two pipelines systems, the Partnership's Year
2000 Readiness Program is being conducted in conjunction with Enbridge
Pipelines.

As at June 30, 1999, all of the Partnership and Enbridge Pipelines' mission
critical systems have been remediated and tested according to the standards
established by the Partnership and Enbridge Pipelines for the Year 2000
Remediation Program. Deployment is complete except for a few systems which will
be put in service by the end of 1999. The Partnership and Enbridge Pipelines
have also addressed substantially all lower priority systems and equipment with
no significant remediation issues encountered. As at the reporting date,
business continuity and contingency plans have been established for mission
critical systems. Formation of a communications network that will be in place
for the year-end rollover with key people on site and additional resources on
call is being developed. In addition, the Partnership and Enbridge Pipelines are
participating in industry task forces on Year 2000 readiness and have met and
continues to monitor critical suppliers and customers.

As at June 30, 1999, the Partnership has incurred $1.5 million of operating and
$0.3 million of capital costs. The Partnership expects that actual costs of the
project will approximate the original cost estimate of $6.0 million referenced
in the Partnership's 1998 Annual Report on Form 10-K.


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

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK
--------------------------------------------------------------------------------

The Partnership's market risk is primarily impacted by changes in interest
rates. The Partnership's market risk with respect to interest rate exposure is
managed through its long-term debt ratio target, its


                                       9
<PAGE>   12

allocation of fixed and floating rate debt and interest rate swap agreements.
Please refer to the Partnership's 1998 Annual Report on Form 10-K, and "Notes to
the Financial Statements", Note 7 "Subsequent Event" of this Form 10-Q.

As the Partnership does not own the crude oil and Natural Gas Liquids ("NGL") it
transports, its cash flows are not significantly impacted by changes in
commodity prices. However, commodity prices have a significant impact on the
underlying supply and demand for crude oil and NGL that the Partnership
transports.

The Partnership has minimal foreign exchange risk.


                                       10
<PAGE>   13

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

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 likely
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.

In a separate action related to the drilling mud discharge in the wetlands area,
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 seeking a civil administrative
penalty for violations of the Clean Water Act resulting from the bentonite
discharges into the wetlands. Representatives of the Partnership have met with
the EPA and are continuing to negotiate with regard to the amount of the penalty
to be assessed and the potential to enter into a Consent Order simultaneously
with the filing of the complaint. It is not anticipated that the penalty will
have a material impact on the financial condition of the Partnership.

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 has also filed suit against the third party to recoup the
penalty and all other costs incurred by the Partnership in connection with the
May 28 release.

The Partnership received a notice dated June 8, 1999, from the Wisconsin
Department of Natural Resources ("WDNR") informing the Partnership that the WDNR
had referred alleged violations of state pollution control regulations to the
Wisconsin Department of Justice for further action. The first violation alleges
that the Partnership failed to monitor discharges of water from SEP II
construction trenches on certain occasions in the summer of 1998 and exceeded
the effluent limitations set forth in a permit. The WDNR had issued a Notice of
Violation on October 29, 1998, with regard to these alleged violations to which
the Partnership had replied on November 10, 1998. The second violation noted in
the June 8 notice alleges that the Partnership had failed to immediately report
a release of NGL's from its Superior, Wisconsin, Terminal in mid-January 1999.
Although it appears likely that a penalty will be assessed, it is not
anticipated that the penalty will have a material impact on the financial
condition of the Partnership.


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<PAGE>   14

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

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K
--------------------------------------------------------------------------------

a)   Exhibits

     27.1 Financial Data Schedule as of and for the six months ended June 30,
          1999.

b)   Reports on Form 8-K

     A report on Form 8-K was filed on April 15, 1999, 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, 1998 and 1997, together with the Report of Independent Public
     Accountants. A report on Form 8-K/A was filed on April 19, 1999, for the
     sole purpose of including the conformed signature that was inadvertently
     omitted from the original filing dated April 15, 1999.

     A report on Form 8-K was filed April 16, 1999, submitting a press release
     dated April 15, 1999, announcing an increase in cash distribution and first
     quarter financial results. A report on Form 8-K/A was filed on April 19,
     1999, for the sole purpose of including the conformed signature that was
     inadvertently omitted from the original filing dated April 16, 1999.


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<PAGE>   15


                                    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)






                                             Dated: August 13, 1999


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