<PAGE>   1

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

(Mark One)

[X]    Quarterly Report Pursuant to Section 13 or 15(d) of the Securities 
       Exchange Act of 1934

For the quarterly period ended September 30, 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 33-16973

                                   NET 1 L.P.
             ------------------------------------------------------
             (Exact name of Registrant as specified in its charter)


                Delaware                                       13-3421566
     ------------------------------                        ----------------
     (State or other jurisdiction of                       (I.R.S. Employer
     incorporation or organization)                       Identification No.)

c/o Lexington Corporate Properties, Inc.
          355 Lexington Avenue
              New York, NY                                       10017
     ------------------------------                           -----------
(Address of principal executive offices)                       (Zip code)

Registrant's telephone number, including area code (212) 692-7200

Securities registered pursuant to Section 12(b) of the Act: None

Securities registered pursuant to Section 12(g) of the Act: Units of Limited
Partnership Interests

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 |_|

State the aggregate market value of the voting stock held by non-affiliates of
the Registrant.

                                 Not Applicable.

There is no active public market for the units of limited partnership interests
issued by the Registrant.
<PAGE>   2

                         PART 1. - FINANCIAL INFORMATION

                          ITEM 1. FINANCIAL STATEMENTS

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                           CONSOLIDATED BALANCE SHEETS

              September 30, 1997 (Unaudited) and December 31, 1996


<TABLE>
<CAPTION>
                                      ASSETS
                                                 September 30,     December 31,
                                                      1997             1996
                                                  ------------     ------------
<S>                                               <C>              <C>         
Real estate, at cost                              $ 26,440,197     $ 22,871,003
Less:  accumulated depreciation                      2,617,384        2,296,399
                                                  ------------     ------------
                                                    23,822,813       20,574,604

Cash and cash equivalents                            1,280,689        2,123,011
Rent receivable                                        378,489          315,325
Other assets                                           160,112          165,963
                                                  ------------     ------------

                                                  $ 25,642,103     $ 23,178,903
                                                  ============     ============

                       LIABILITIES AND PARTNERS' CAPITAL


Mortgage notes payable                            $  5,754,263     $  3,551,850
Accrued interest payable                                30,429           31,631
Accounts payable and other liabilities                 117,607           87,007
                                                  ------------     ------------
                                                     5,902,299        3,670,488
                                                  ------------     ------------

Partners' capital (deficit):
    General Partner                                   (175,615)        (180,243)
    Limited Partners ($1,000 per Unit,
    50,000 Units authorized, 30,772
    Units issued and outstanding)                   19,915,419       19,688,658
                                                  ------------     ------------

    Total partners' capital                         19,739,804       19,508,415
                                                  ------------     ------------

                                                  $ 25,642,103     $ 23,178,903
                                                  ============     ============
</TABLE>

     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   3

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                        CONSOLIDATED STATEMENTS OF INCOME

                 Quarters Ended September 30, 1997 and 1996 and
                  Nine Months Ended September 30, 1997 and 1996
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                  Nine Months     Nine Months
                                  Quarter Ended   Quarter Ended     Ended           Ended
                                   September 30,  September 30,   September 30,  September 30,
                                      1997           1996            1997            1996
                                    --------      ----------      ----------      ----------
<S>                                 <C>           <C>             <C>             <C>       
Revenues:
   Rental                           $701,051      $  598,438      $2,250,192      $2,068,393
   Interest and other                 17,530          42,199          69,942          81,033
                                    --------      ----------      ----------      ----------
                                     718,581         640,637       2,320,134       2,149,426
                                    --------      ----------      ----------      ----------

Expenses:
   Interest expense                  134,708          96,390         336,240         292,387
   Depreciation                      118,069          98,136         320,985         294,408
   General, administrative,
       and other                      58,199          51,074         253,078         192,452
                                    --------      ----------      ----------      ----------
                                     310,976         245,600         910,303         779,247
                                    --------      ----------      ----------      ----------

Net income                          $407,605      $  395,037      $1,409,831      $1,370,179
                                    ========      ==========      ==========      ==========

Net income per Unit of limited
   partnership interest             $  12.98      $    12.58      $    44.90      $    43.64
                                    ========      ==========      ==========      ==========
</TABLE>

     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   4

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                      CONSOLIDATED STATEMENTS OF CASH FLOWS

                  Nine months ended September 30, 1997 and 1996
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                       Nine Months Ended   Nine Months Ended
                                                         September 30,      September 30,
                                                             1997              1996
                                                          -----------       -----------
<S>                                                       <C>               <C>        
Cash flows from operating activities:
    Net income                                            $ 1,409,831       $ 1,370,179
    Adjustments to reconcile net income to
        net cash provided by operating activities:
        Depreciation                                          320,985           294,408
        Other, net                                            (29,037)          (29,063)
                                                          -----------       -----------
        Total adjustments                                     291,948           265,345
                                                          -----------       -----------

    Net cash provided by operating activities               1,701,779         1,635,524
                                                          -----------       -----------

Cash flows from investing activities:
    Principal payments received on note receivable              1,122               814
    Acquisition of Texas Property, net of
        mortgage liability assumed                         (1,204,245)               --
                                                          -----------       -----------
    Net cash used in investing activities                  (1,203,123)              814
                                                          -----------       -----------

Cash flows from financing activities:
    Principal payments on mortgage notes                     (162,536)          (99,693)
    Cash distributions to partners                         (1,178,442)       (1,178,442)
                                                          -----------       -----------
    Net cash used in financing activities                  (1,340,978)       (1,278,135)
                                                          -----------       -----------

Net (decrease) increase in cash and cash equivalents         (842,322)          358,203

Cash and cash equivalents at beginning of period            2,123,011         1,816,179
                                                          -----------       -----------

Cash and cash equivalents at end of period                $ 1,280,689       $ 2,174,382
                                                          ===========       ===========


Supplemental disclosure of cash flow information:

Cash payments for interest                                $   337,442       $   264,851
                                                          ===========       ===========
</TABLE>


Supplemental disclosure of non-cash investing and financing activities:

On May 30, 1997, in connection with the acquisition of the Texas Property, the
Partnership assumed approximately $2.4 million of first mortgage financing.

     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   5

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                               September 30, 1997
                                   (Unaudited)

1.       The Partnership and Basis of Presentation

         Net 1 L.P. (the "Partnership") was formed as a limited partnership on
         August 25, 1987 under the laws of the State of Delaware to invest in
         real estate or interests therein to be net leased to corporations or
         other entities.

         As of September 30, 1997, the Partnership has a total of 30,772 Units
         issued and outstanding held by approximately 1,720 limited partners.

         The unaudited financial statements reflect all adjustments that are, in
         the opinion of the General Partner, necessary to a fair statement of
         the results for the interim period presented. For a more complete
         understanding of the Partnership's financial position and accounting
         policies, reference is made to the financial statements previously
         filed with the Securities and Exchange Commission with the
         Partnership's Annual Report on Form 10-K for the year ended December
         31, 1996.

2.       Summary of Significant Accounting Policies

         On January 1, 1996, the Partnership adopted SFAS No. 121, "Accounting
         for the Impairment of Long-Lived Assets and for Long-Lived Assets to be
         Disposed of." This SFAS establishes the recognition and measurement
         criteria for impairment losses on long-lived assets, certain
         identifiable intangibles and goodwill related to those assets to be
         held and used and for long-lived assets and certain identifiable
         intangibles to be disposed of. This SFAS requires that an impairment
         loss be recognized when events or changes in circumstances indicate
         that the carrying amount of an asset may not be recoverable.

         For purposes of the statement of cash flows, the Partnership considers
         all highly liquid instruments to be cash equivalents. The balance sheet
         caption, cash and cash equivalents, includes $1.28 million of money
         market instruments at September 30, 1997.

         The leases relating to the properties are operating leases in
         accordance with SFAS 13. Rental revenue is recognized on a
         straight-line basis over the minimum lease terms. At September 30,
         1997, the Partnership's rent receivable primarily consists of amounts
         for the excess of rental revenues recognized on a straight-line basis
         over the rents' collectible under the leases.

         The net income per Unit of limited partnership interest was calculated
         by using the actual number of Units outstanding for each period and
         allocating the income attributable for that period to the Limited
         Partners. The weighted average number of Units outstanding was 30,772
         during each of the quarters and nine months ended September 30, 1997
         and 1996.

         Certain amounts included in the prior years' financial statements have
         been reclassified to conform with the current year's presentation.
<PAGE>   6

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

2.       Continued

         Management of the Partnership has made a number of estimates and
         assumptions relating to the reporting of assets and liabilities and the
         disclosure of contingent assets and liabilities to prepare these
         financial statements in conformity with generally accepted accounting
         principles. Actual results could differ from those estimates.

3.       The Partnership Agreement

         For financial statement reporting purposes all items of income are
         allocated in the same proportion as distributions of distributable
         cash.

         As of September 30, 1997, the Partnership has made cumulative cash
         distributions to the Limited Partners totaling $20,286,623. The unpaid
         cumulative preferred return at September 30, 1997 totaled $10,394,695
         ($340.43 to $334.58 per Unit).

         On October 31, 1997, the cumulative preferred return that was unpaid at
         September 30, 1997 was reduced by a cash distribution for the quarter
         ended September 30, 1997 totaling $384,958 or $12.51 per Unit to the
         Limited Partners and $7,856 to the General Partner.

4.       Mortgage Notes Payable

         Principal paydowns of the mortgage notes payable for the succeeding
         five years are as follows:

<TABLE>
<CAPTION>
                  Year Ending
                  December 31,                                  Amount
                  ------------                                  ------

                  <S>                                  <C>
                  1997 (3 months)                      $        88,657
                  1998                                         377,126
                  1999                                         416,056
                  2000                                         459,251
                  2001                                         507,207
                  2002                                         560,475
                                                               =======
</TABLE>

5.       Properties

         On May 30, 1997, the Partnership acquired a property located in
         Brownsville, Texas (the "Texas Property") from an unrelated party. The
         Texas Property consists of an 85,334 square foot warehouse style retail
         store building leased to Wal-Mart Stores, Inc. pursuant to a triple net
         lease.
<PAGE>   7

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

5.       Continued

         The lease has a remaining term which expires on January 31, 2008. The
         lease provides for annual base rental payments of $320,513, or $3.76
         per square foot. In addition to net rent, Wal-Mart is required to pay
         percentage rent equal to 1% of gross sales in excess of base gross
         receipts as defined, during the fiscal year February 1 to January 31,
         payable on April 1. The lease has five renewal terms of five years
         each.

         The purchase price of $3,525,000 and related expenses of approximately
         $44,000 were satisfied by a cash payment and by an assumption of an
         existing note with a principal balance of $2,364,949. The note bears
         interest at a rate of 7.35% per annum, with a monthly debt service
         payment of principal and interest in the amount of $26,709 to fully
         amortize the note on January 15, 2008.

         The following unaudited pro forma consolidated operating information
         for the nine months ended September 30, 1997 and September 30, 1996
         were prepared as if the above acquisition had been consummated as of
         January 1, 1997 and January 1, 1996, respectively.  The information
         provided do not purport to be indicative of what the operating results
         of the Partnership would have been had the acquisition been consumated
         on the dates assumed.  The pro forma amounts are as follows:    
                                                 

<TABLE>
<CAPTION>
                                            Unaudited Pro Forma             Historical
                                               Quarter ended              Quarter ended 
                                        September 30, September 30,    September 30, September 30
                                           1997          1996             1997          1996
                                           ----          ----             ----          ----
<S>                                       <C>          <C>              <C>             <C>   
         Revenues                          $2,451,958   $2,389,811       $2,320,134      $2,149,426
         Net income                        $1,439,973   $1,420,728       $1,409,831      $1,370,179
         Net income per Unit
           of limited
           partnership interest            $    45.76   $    45.25       $    44.90      $    43.64
</TABLE>

         Minimum total annual future rental payments receivable under the
         noncancelable operating leases for the properties as of September 30,
         1997, follow:

<TABLE>
<CAPTION>
                        Year Ending
                        December 31,                         Amount
                        ------------                         ------
                        <S>                       <C>
                        1997 (3 months)           $         679,995
                        1998                              2,752,426
                        1999                              2,797,849
                        2000                              2,797,849
                        2001                              2,799,102
                        2002                              2,812,875
                        Thereafter                       16,024,141
                                                         ----------

                                                  $      30,664,237
                                                         ==========
</TABLE>

         The leases are triple net leases requiring the lessees to pay all
         taxes, insurance, maintenance, and all other similar charges and
         expenses relating to the properties and their use and occupancy.
<PAGE>   8

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

6.       Related Party Transactions

         Leased Properties Management, Inc., an affiliate of the General
         Partner, is entitled to receive a fee for managing the Partnership's
         properties in the amount of 1% of gross annual rental receipts (or a
         greater amount in certain circumstances). As of September 30, 1997, a
         property management fee of $21,870 had been paid or accrued to Leased
         Properties Management, Inc.
<PAGE>   9

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

Liquidity and Capital Resources

On May 30, 1997, the Partnership acquired a property located in Brownsville,
Texas (the "Texas Property") from an unrelated party. The Texas Property
consists of an 85,334 square foot warehouse style retail store building leased
to Wal-Mart Stores, Inc. pursuant to a triple net lease.

The lease has a remaining term which expires on January 31, 2008. The lease
provides for annual base rental payments of $320,513, or $3.76 per square foot.
In addition to net rent, Wal-Mart is required to pay percentage rent equal to 1%
of gross sales in excess of base gross receipts as defined, during the fiscal
year February 1 to January 31, payable on April 1. The lease has five renewal
terms of five years each.

The purchase price of $3,525,000 and related expenses of approximately $44,000
were satisfied by a cash payment and by an assumption of an existing note with a
principal balance of $2,364,949. The note bears interest at a rate of 7.35% per
annum, with a monthly debt service payment of principal and interest in the
amount of $26,709 to fully amortize the note on January 15, 2008.

As of September 30, 1997, the Partnership has made cumulative cash distributions
to the Limited Partners totaling $20,286,623. The unpaid cumulative preferred
return at September 30, 1997 totaled $10,394,695 (see note 3 of Notes to
Consolidated Financial Statements).

The Partnership attempts to maintain a working capital reserve in an amount
equal to 3% of the gross proceeds of its offering, an amount that is anticipated
to be sufficient to satisfy liquidity requirements. Liquidity could be adversely
affected by unanticipated costs, particularly costs relating to the vacancy of
properties, tenants experiencing financial difficulties, and greater than
anticipated operating expenses. To the extent that such working capital reserves
are insufficient to satisfy the cost requirements of the Partnership, additional
funds may be obtained through short-term or permanent loans or by reducing
distributions to limited partners.

There are no material restrictions (other than the debt service requirements
under the mortgage notes) upon the Partnership's present or future ability to
make distributions in accordance with the provisions of its Partnership
Agreement.
<PAGE>   10

Results of Operations

The results of operations for the quarter and nine months ended September 30,
1997 (see Consolidated Statements of Income) are attributable to the acquisition
and operation of the twenty-four real property investments purchased from 1988
to 1997, and interest earned on interest-bearing bank investments.

Total revenues for the quarter and nine months ended September 30, 1997
increased $77,944 and $170,708 from the same periods in 1996. Rental revenues
for the nine months ended September 30, 1997 and 1996 included percentage rent
received during the first quarter of each of these periods in the amounts of
$278,684 and $273,080, respectively. Rental revenues for the quarter and nine
months ended September 30, 1997 increased $102,613 and $181,799 primarily due to
rent received on the Texas Property acquired on May 30, 1997. Interest and other
revenues for the quarter and nine months ended September 30, 1997 decreased from
1996, due to fluctuating cash balances maintained.

Total expenses for the quarter and nine months ended September 30, 1997
increased $65,376 and $131,056 from the same periods in 1996 due to increases in
interest expense, depreciation and general and administrative expenses. The
increases in interest expense are primarily due to the assumption of a mortgage
note in connection with the acquisition of the Texas Property in May 1997. The
increases in depreciation are primarily due to the acquisition of the Texas
Property in May 1997. The increase in general and administrative expenses for
the nine months period is primarily due to property appraisals incurred in 1997.

Net income for the quarter and nine months ended September 30, 1997, did not
materially change from the same periods in 1996.

In February 1997, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 128, Earnings Per Share ("SFAS No. 128").
SFAS No. 128 supersedes Accounting Principles Board Opinion No. 15, Earnings Per
Share ("APB 15") and specifies the computation, presentation, and disclosure
requirements for earnings per share ("EPS") for entities with publicly held
common stock or potential common stock. SFAS No. 128 replaces the presentation
of primary EPS with a presentation of basic EPS and fully diluted EPS with
diluted EPS. It also requires dual presentation of basic and diluted EPS on the
face of the income statement for all entities with complex capital structures
and requires a reconciliation of the numerator and denominator of the basic EPS
computation to the numerator and denominator of the diluted EPS computation.
This statement will be adopted for both interim and annual period ending after
December 15, 1997. The adoption of this SFAS would have had no effect on the
Partnership's net income per unit for the quarter and nine months ended
September 30, 1997.
<PAGE>   11

                           PART II - OTHER INFORMATION


ITEM 1.    Legal Proceedings - not applicable.

ITEM 2.    Changes in Securities - not applicable.

ITEM 3.    Defaults under the Senior Securities - not applicable.

ITEM 4.    Submission of Matters to a Vote of Security Holders - not applicable.

ITEM 5.    Other Information - not applicable.

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

                  (a)      Exhibits.

                           Exhibit No.           Exhibit
                           -----------           -------
                                27               Financial Data Schedule

                  (b)      Reports on form 8-K filed during the quarter ended 
                           September 30, 1997.

                           None.
<PAGE>   12

                                   SIGNATURES

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.

                                                  NET 1 L.P.

                                                  By:   Lepercq Net 1 L.P.
                                                        its general partner

                                                  By:   Lepercq Net 1 Inc.
                                                        its general partner


Date: November 14, 1997                           By:   /s/ E. Robert Roskind
      --------------------------                      --------------------------
                                                        E. Robert Roskind
                                                        President