<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, 1997

                                       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 20,090,000 Class A Common units outstanding as at May 5,
1997.





<PAGE>   2

                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                        
                                                                                                   PAGE
                                                                                                    ----
                         PART I. FINANCIAL INFORMATION
<S>            <C>
ITEM 1.        Financial Statements

                 Consolidated Statement of Income
                   for the three-month periods ended March 31, 1997 and 1996 . . . . . . . . . . .   1                    


                 Consolidated Statement of Cash Flows
                  for the three-month periods ended March 31, 1997 and 1996  . . . . . . . . . . .   2

                 Consolidated Statement of Financial Position
                   as at March 31, 1997 and December 31, 1996 .  . . . . . . . . . . . . . . . . .   3

                 Consolidated Statement of Partners' Capital
                   for the period ended March 31, 1997  . . . . . . . . . . . . . . . . . . . . .    4

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


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


                           PART II. OTHER INFORMATION


ITEM 6.        Exhibits and Reports on Form 8-K . . . . . . . . . . . . . . . . . . . . . . . . .    7

SIGNATURE      .....  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .    8
</TABLE>

When used in this document, the words "anticipate," "believe," "expect,"
"estimate," and similar expressions are intended to identify forward-looking
statements.  Such statements are subject to certain risks, uncertainties and
assumptions.  Should one or more of these risks or uncertainties materialize,
or should underlying assumptions prove incorrect, actual results may vary
materially from those anticipated, believed, expected or estimated.  For
additional discussion of such risks, uncertainties and assumptions, see the
Partnership's 1996 Annual Report on Form 10-K.

                                        
<PAGE>   3


PART I - FINANCIAL INFORMATION
--------------------------------------------------------------------------------
ITEM 1.  FINANCIAL STATEMENTS
--------------------------------------------------------------------------------


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


--------------------------------------------------------------------------------
<TABLE>
<CAPTION>
                                                                                           Three months ended
                                                                                                March 31,
(unaudited; dollars in millions, except per unit amounts)                                  1997          1996
-------------------------------------------------------------------------------------------------------------------
<S>                                                                                    <C>            <C>

Operating Revenue                                                                      $    68.7      $    68.0
----------------------------------------------------------------------------------------------------------------------
                                                                                              
Expenses                                                                                      
  Power                                                                                     17.1           16.5
  Operating and administrative                                                              16.1           16.3
  Depreciation                                                                               9.8            9.9
  Provision for prior years' rate refunds (Note 4)                                             -           20.1
----------------------------------------------------------------------------------------------------------------------
                                                                                            43.0           62.8
----------------------------------------------------------------------------------------------------------------------
                                                                                              
Operating Income                                                                            25.7            5.2
                                                                                                         
Interest Income                                                                              2.3            2.2
                                                                                              
Interest Expense                                                                           (10.1)         (13.8)
                                                                                              
Minority Interest                                                                           (0.2)           0.1
----------------------------------------------------------------------------------------------------------------------
                                                                                              
Net Income (Loss) (Note 4)                                                             $    17.7      $    (6.3)
----------------------------------------------------------------------------------------------------------------------
                                                                                              
Net Income (Loss) Per Unit (Note 2)                                                    $     0.71     $    (0.27)
----------------------------------------------------------------------------------------------------------------------
                                                                                              
Cash Distributions Paid Per Unit (Note 3)                                              $     0.68     $     0.64
======================================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.






                                       1
<PAGE>   4


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



<TABLE>
<CAPTION>
                                                                                           Three months ended
                                                                                                 March 31,
(unaudited; dollars in millions)                                                              1997       1996
--------------------------------------------------------------------------------------------------------------------------
<S>                                                                                      <C>           <C>
Operating Activities
  Net income (loss)                                                                      $    17.7     $    (6.3)
  Adjustments to reconcile net income (loss) to                                                 
    cash provided from operating activities:                                                    
       Depreciation                                                                            9.8           9.9
       Accrued rate refunds and related interest (Note 4)                                      1.0          28.8
       Other                                                                                  (0.2)          0.2
       Changes in operating assets and liabilities:                                             
          Accounts receivable and other                                                        1.1          (2.6)
          Materials and supplies                                                              (0.2)           -
          General Partner and affiliates                                                      (0.9)          1.0
          Accounts payable and other                                                          (7.2)         (1.5)
          Interest payable                                                                     8.6           7.2
          Property and other taxes                                                             1.9           2.0
          Payment of rate refunds and related interest (Note 4)                               (6.7)           -
-----------------------------------------------------------------------------------------------------------------------------
                                                                                              24.9          38.7
-----------------------------------------------------------------------------------------------------------------------------
                                                                                                
Investing Activities                                                                            
  Additions to property, plant and equipment                                                 (15.4)         (5.5)
  Short-term investments, net                                                                  6.5         (13.0)
-----------------------------------------------------------------------------------------------------------------------------
                                                                                                
                                                                                              (8.9)        (18.5)
-----------------------------------------------------------------------------------------------------------------------------
                                                                                                
Financing Activities                                                                            
  Distributions to partners                                                                  (16.8)        (15.7)
  Minority interest                                                                           (0.2)         (0.2)
-----------------------------------------------------------------------------------------------------------------------------
                                                                                                
                                                                                             (17.0)        (15.9)
-----------------------------------------------------------------------------------------------------------------------------
                                                                                                
Increase (Decrease) in Cash and Cash Equivalents *                                            (1.0)          4.3
                                                                                                
Cash and Cash Equivalents at Beginning of Period                                              89.6          77.0
-----------------------------------------------------------------------------------------------------------------------------
                                                                                                
Cash and Cash Equivalents at End of Period                                               $    88.6     $    81.3
=============================================================================================================================    
</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
  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>
                                                                                   March 31,      December 31,
(unaudited, except for December 31, 1996; dollars in millions)                       1997             1996
------------------------------------------------------------------------------------------------------------------------------
<S>                                                                                <C>               <C>

                                                    ASSETS
Current Assets
  Cash and cash equivalents                                                        $   88.6          $   89.6
  Short-term investments                                                               77.2              83.7
  Accounts receivable and other                                                        26.1              27.2
  Materials and supplies                                                                7.2               7.0
------------------------------------------------------------------------------------------------------------------------------

                                                                                      199.1             207.5
------------------------------------------------------------------------------------------------------------------------------

Deferred Charges and Other                                                              5.3               4.9
------------------------------------------------------------------------------------------------------------------------------

Property, Plant and Equipment
  At cost                                                                             899.5             884.2
  Accumulated depreciation                                                           (130.4)           (120.7)
------------------------------------------------------------------------------------------------------------------------------

                                                                                      769.1             763.5
------------------------------------------------------------------------------------------------------------------------------

                                                                                   $  973.5          $  975.9
===============================================================================================================================



                                       LIABILITIES AND PARTNERS' CAPITAL
Current Liabilities
  Due to General Partner and affiliates                                            $    0.6          $    1.5
  Accounts payable and other                                                            9.6              16.8
  Interest payable                                                                     11.8               3.2
  Property and other taxes                                                             13.0              11.1
  Current portion of accrued rate refunds and related interest                         29.0              29.0
-------------------------------------------------------------------------------------------------------------------------------

                                                                                       64.0              61.6

Long-Term Debt                                                                        463.0             463.0
Accrued Rate Refunds and Related Interest (Note 4)                                     44.6              50.3
Minority Interest                                                                       1.4               1.4
Contingencies (Note 5)
-------------------------------------------------------------------------------------------------------------------------------

                                                                                      573.0             576.3
-------------------------------------------------------------------------------------------------------------------------------

Partners' Capital
  General Partner                                                                       1.7               1.6
  Class B Common Unitholder (units issued - 3,912,750) (Note 6)                        22.3              21.7
  Class A Common Unitholders (units issued - 20,090,000) (Note 6)                     376.5             376.3
-------------------------------------------------------------------------------------------------------------------------------

                                                                                      400.5             399.6
-------------------------------------------------------------------------------------------------------------------------------

                                                                                   $  973.5          $  975.9
===============================================================================================================================
</TABLE>

See accompanying notes to the consolidated financial statements.





                                      3
<PAGE>   6


                       LAKEHEAD PIPE LINE PARTNERS, L.P.
                  CONSOLIDATED STATEMENT OF PARTNERS' CAPITAL


<TABLE>
<CAPTION>
                                                                    Class B          Class A
(unaudited, except for December 31, 1996;            General         Common           Common
 dollars in millions)                                Partner     Unitholder      Unitholders           Total
-------------------------------------------------------------------------------------------------------------------------------
<S>                                                <C>            <C>             <C>              <C>
Partners' Capital at December 31, 1996             $    1.6       $    21.7       $    376.3       $    399.6

Net Income Allocation                                   0.6             3.3             13.8             17.7
                                                                           
Distributions to Partners                              (0.5)           (2.7)           (13.6)           (16.8)
-------------------------------------------------------------------------------------------------------------------------------

Partners' Capital at March 31, 1997                $    1.7       $    22.3       $    376.5       $    400.5
================================================================================================================================
</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, consisting of normal
     recurring adjustments and a non-recurring adjustment to the first quarter
     of 1996 to reflect a tariff rate agreement approved by the Federal Energy
     Regulatory Commission in October 1996, which management considers
     necessary to present fairly the financial position as at March 31, 1997
     and December 31, 1996; the results of operations for the three month
     periods ended March 31, 1997 and 1996; and cash flows for the three month
     periods ended March 31, 1997 and 1996.  The results of operations for the
     three months ended March 31, 1997 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 1996 Annual Report on Form 10-K.
                
2.   Net Income Per Unit

     Net income per unit is computed by dividing net income, after deduction of
     the General Partner's allocation, by the total number of Class A
     and Class B Common units outstanding (24,002,750).

3.   Cash Distribution

     On April 15, 1997, the Board of Directors of the General Partner declared a
     cash distribution for the quarter ended March 31, 1997 of $0.68 per unit. 
     The distribution will be made on May 15, 1997 to Unitholders of record on
     April 30, 1997.  
        




                                      4
<PAGE>   7


4.   Accrued Rate Refunds and Related Interest

     Results for the first quarter of 1996 were restated to reflect the rate
     refunds and related interest accrued in response to the 1996 tariff rate
     agreement which were applicable to the first quarter of 1996 and prior
     years. Net income for the first quarter of 1996 was therefore reduced by
     $23.0 million, or $0.95 per unit, from that previously reported.  As
     provided in the 1996 tariff rate agreement, refunds are being paid through
     a 10% reduction on current rates. This reduction will continue until all
     refunds have been made, which is estimated to take another 2.5 years. 
     With the exception of interest that continues to accrue on the unpaid
     balance, all rate refunds and related interest due as a result of the
     agreement were accrued and reflected in net income prior to 1997.
        
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 crude oil 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 or 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.   Common Units

     As previously announced, the period during which the Partnership's
     Preference units had certain cash distribution priorities over the
     Partnership's Common units expired with the distribution paid in February
     1997.  Going forward, all Partnership units will have equal rights with
     respect to cash distributions. To more accurately reflect this status, the
     Preference units have been renamed Class A Common units and the existing
     Common units have been renamed Class B Common units.  This is only a name
     change and does not affect any Unitholder's ownership rights in the
     Partnership. There is no need to exchange Preference unit certificates for
     Class A Common unit certificates, as they will automatically be treated as
     such.
        


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

RESULTS OF OPERATIONS

Net income for the first quarter of 1997 was $17.7 million, or $0.71 per unit,
an increase of $0.9 million, or $0.03 per unit, over the "recalculated" net
income for the first quarter of 1996.  The first three months of last year
included provisions for prior years' rate refunds ($20.1 million) and interest
($3.2 million) recorded to reflect the retroactive aspects of the 1996 tariff
rate agreement between the Partnership and customer representatives.  Excluding
these provisions, recalculated net income for the first quarter of 1996 was
$16.8 million, or $0.68 per unit.  Net income for the first quarter of 1997 was
higher than 1996's recalculated amount largely due to lower interest expense.

Operating revenue increased slightly, primarily due to a greater proportion of
heavy crude oil 



                                      5
<PAGE>   8


deliveries, up 30% to 562,000 barrels per day.  Because heavy
crude oil is more expensive to pump due to its higher viscosity, the tariff
rate for heavy crude oil is greater than that for lighter crude oils.
Deliveries averaged 1,502,000 barrels per day for the first quarter of 1997, up
4% from the 1,445,000 averaged for the first quarter of last year.  System
utilization, measured in barrel miles, decreased slightly from last year's
first quarter, reflecting a higher proportion of shorter haul deliveries to the
significant Midwest markets served by the Partnership.

Excluding the provision for prior years' rate refunds ($20.1 million) from
1996, total first quarter operating expenses were slightly higher than the same
period of 1996 due to increased power costs.  The increase resulted from the
transportation of greater amounts of heavy crude oil.  Depreciation expense was
essentially unchanged despite growth in property, plant and equipment, due to
the impact of new depreciation rates put in effect July 1, 1996 to better
represent the service life of the pipeline system.

Excluding the provision for interest related to prior years ($3.2 million),
interest expense for the first quarter was less than the first quarter of 1996
due to lower interest rates and balances with respect to rate refunds payable,
partially offset by additional borrowings under the Partnership's credit
facility (primarily to finance the 1996 expansion).

LIQUIDITY AND CAPITAL RESOURCES

At March 31, 1997, cash, cash equivalents and short-term investments totaled
$165.8 million, down $7.5 million since December 31, 1996, as cash required for
distributions and capital expenditures exceeded cash generated from operating
activities.  Of this $165.8 million, $17.0 million ($0.68 per unit) was set
aside for the cash distribution payable May 15, 1997 with the remaining $148.8
million available for capital expenditures, distributions or other business
needs.

Cash flow from operating activities for the first quarter of 1997 decreased
$13.8 million from the corresponding 1996 period, primarily due to the payment
of rate refunds and interest in 1997 ($6.7 million) and the collection of
operating revenue in 1996 that was subject to refund ($3.8 million).

First quarter capital expenditures totaled $15.4 million, of which $4.8 million
was for the expansion program consisting primarily of a new pipeline from
Superior, Wisconsin to the Chicago area.  The General Partner believes that the
majority of the expenditures for construction of this new pipeline will be
incurred in 1998, with completion planned for the second half of that year.
The Partnership plans on financing this expansion with existing cash balances,
borrowings and proceeds from the issuance of additional Partnership units.
Excluding expenditures for the new pipeline, the Partnership expects 1997
capital expenditures to total approximately $40 million.  These expenditures
are expected to be financed with existing cash or borrowed funds.

GENERAL

On April 10, 1997, the Partnership, in conjunction with its Canadian affiliate
Interprovincial Pipe Line Inc., announced a four-stage program to increase
western Canadian crude oil pipeline capacity that could ultimately provide an
additional 520,000 barrels per day at an estimated cost of Cdn. $875 million.
Although the majority of the expenditures will be spent in Canada by
Interprovincial, approximately Cdn. $225 million, or U.S. $170 million, is
projected to be spent by the Partnership. The first stage would provide 120,000
barrels per day of new capacity at a cost of Cdn. $100 million to be
operational in 1999.  It would be followed by a second stage of 80,000 barrels
per day costing Cdn. $175 million to be in service in 2000, and a third stage
of 70,000 barrels per day costing Cdn. $100 million for completion in 2001.
The final phase of Cdn. $500 million would provide an additional 250,000
barrels per day beyond 2001.  This program is in addition to the current
expansion which consists primarily of a new pipeline from Superior to the
Chicago area.


                                      6

<PAGE>   9
--------------------------------------------------------------------------------
PART II - OTHER INFORMATION
--------------------------------------------------------------------------------

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

a)  Exhibits

    4.1      Form of Certificate representing Class A Common units.
             (Registrant's Form 8-A/A, dated May 2, 1997)*

    4.2      Amended and Restated Agreement of Limited Partnership of the
             Partnership, dated April 15, 1997.  (Registrant's Form 8-A/A,
             dated May 2, 1997)*

    27.1     Financial Data Schedule as of and for the three months ended March
             31, 1997.

    *Incorporated herein by reference to the document identified in
     parentheses.

b)  Reports on Form 8-K

    No reports on Form 8-K were filed during the quarter ended March 31, 1997.





                                       7
<PAGE>   10



                                   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/ S.Q. DeVinck
                                      ----------------------------------------
                                                  S.Q. DeVinck
                                                 Chief Accountant 
                                              (Principal Financial and
                                                 Accounting Officer)





                                                  May 5, 1997


                                      8