<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 period ended June 30, 2000

                                       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 Trust
          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
                 (Dollars in thousands, except per Unit amounts)

                 June 30, 2000 (Unaudited) and December 31, 1999

<TABLE>
<CAPTION>


                                                  June 30,    December 31,
                  Assets                            2000          1999
                  ------                            ----          ----

<S>                                                <C>         <C>
Real estate, at cost                               $46,593     $ 38,711
   Less: accumulated depreciation                    2,906        2,483
                                                   -------      -------
                                                    43,687       36,228

Cash and cash equivalents                            2,121        1,951
Restricted cash                                      1,644        1,710
Deferred expenses (net of accumulated
   amortization of $1 in 2000)                          49          -
Rent receivable                                        600          504
Other assets                                           268          528
                                                   -------      -------

                                                   $48,369     $ 40,921
                                                    ======       ======



     Liabilities and Partners' Capital
     ---------------------------------

Mortgages and notes payable                        $23,696     $ 16,272
Accrued interest payable                               165           88
Accounts payable and other liabilities                 438          912
                                                   --------    --------
                                                    24,299       17,272
                                                   -------      -------

Partners' capital (deficit):
General Partner                                        (88)         (96)
Limited Partners ($1,000 per Unit, 50,000 Units
  authorized, 30,772 Units issued and outstanding)  24,158       23,745
                                                    ------       ------
   Total partners' capital                          24,070       23,649
                                                    ------       ------

                                                   $48,369     $ 40,921
                                                    ======       ======

</TABLE>

     See accompanying notes to unaudited consolidated financial statements.


<PAGE>   3

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                        CONSOLIDATED STATEMENTS OF INCOME
                 (Dollars in thousands, except per Unit amounts)

                Three and Six Months Ended June 30, 2000 and 1999
                                   (Unaudited)
<TABLE>
<CAPTION>



                                 Three Months Ended       Six Months Ended
                                      June 30,                June 30,
                                  2000       1999         2000        1999
                                  ----       ----         ----        ----

<S>                              <C>       <C>           <C>         <C>
Revenues:
  Rental                         $1,022    $  702        $2,462      $1,829
  Interest and other                 61        19           102          39
                                 -------    ------        ------      -------
                                  1,083       721         2,564       1,868
                                 -------    ------        ------      -------
Expenses:
  Interest expense                  416       120           750         242
  Depreciation and amortization     224        93           424         211
  General, administrative and other  80       113           183         232
                                 -------    ------        ------      -------
                                    720       326         1,357         685
                                 -------    ------        ------      -------
Income before gain on sale
  of properties                     363       395         1,207       1,183
  Gain on sale of properties         -      2,668             -       2,668
                                 -------    -----        --------     -----

Net income                       $  363    $3,063        $1,207      $3,851
                                  =====     =====         =====       =====

Net income per Unit of limited
  partnership interest           $11.56    $97.55        $38.43      $122.65
                                  =====     =====         =====       ======

</TABLE>


     See accompanying notes to unaudited consolidated financial statements.



<PAGE>   4


                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                             (Dollars in thousands)

                     Six Months Ended June 30, 2000 and 1999
                                   (Unaudited)

<TABLE>
<CAPTION>


                                                          2000        1999
                                                          ----        ----
<S>                                                    <C>           <C>
Net cash provided by operating activities              $  1,464      $ 1,190
                                                       ----------    ------

Cash flows from investing activities:
  Investment in real estate                                (137)        -
  Proceeds from sale of properties, net                       -       8,588
  Increase in restricted cash                                 -      (8,709)
                                                       ----------    ------
  Net cash used in investing activities                    (137)       (121)
                                                       ----------    ------

Cash flows from financing activities:
  Principal payments on mortgage notes                     (321)       (179)
  Increase in deferred expenses                             (50)        -
  Cash distributions to partners                           (786)       (786)
                                                       ----------    ------
  Net cash used in financing activities                  (1,157)       (965)
                                                       ----------    ------

Change in cash and cash equivalents                         170         104
Cash and cash equivalents at beginning of period          1,951       1,688
                                                       ----------    ------
Cash and cash equivalents at end of period             $  2,121      $1,792
                                                        ========     ======

Supplemental disclosure of cash flow information:
Cash paid during the period for interest               $    673      $  243
                                                            ===         ===
</TABLE>

Supplemental disclosure of non-cash investing and financing activities:
In 2000, in connection with the acquisition of a property in Henderson, North
Carolina, the Partnership assumed approximately $4.68 million of first
mortgage financing and issued a promissory note of approximately $3.07
million.

     See accompanying notes to unaudited consolidated financial statements.


<PAGE>   5

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                                  June 30, 2000
                                   (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
      net leased real estate properties or interests therein.  As of June 30,
      2000, the Partnership had owned interests in nine properties.

      As of June 30, 2000, the Partnership has a total of 30,772 Units issued
      and outstanding held by approximately 1,400 limited partners.

      The unaudited financial statements reflect all adjustments that are, in
      the opinion of the General Partner, necessary to present a fair
      statement of condition and 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, 1999.

2.    Summary of Significant Accounting Policies
      -----------------------------------------

      Net income per Unit amounts were calculated by using the weighted
      average number of Units outstanding for each period and allocating 98%
      of the income attributable for that period to the Limited Partners.
      The weighted average number of Units outstanding was 30,772 for all
      periods presented.

      Management of the Partnership has made a number of estimates and
      assumptions relating to the reporting of assets and liabilities, the
      disclosure of contingent assets and liabilities and the reported
      amounts of revenues and expenses 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.

      Distributable cash attributed to a particular limited partner's Unit is
      calculated from the date of admission to the Partnership.  The unpaid
      cumulative preferred return at June 30, 2000 totaled $15.469 million
      ($499.47 to $505.32 per Unit, per close).  On July 31, 2000, the unpaid
      cumulative preferred return was reduced by a cash distribution to the
      Limited Partners totaling $384,958 ($12.51 per Unit).  The General
      Partner received a cash distribution of $7,856 in July 2000.



<PAGE>   6
                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



4.    Properties
      ----------

      During the six months ended June 30, 2000, the Partnership entered into
      the following real estate transaction:
<TABLE>
<CAPTION>

                                                                                                            Lease            Net
                                                                     Capitalized         Annualized       Expiration       Rentable
      Date of                                                           Costs             Base Rent         Date           Square
      Transaction        Tenant                      Location         ($000's)             ($000's)       (month/year)       Feet
      -----------        ------                      --------         --------             --------        ----------        ----
<S>                  <C>                          <C>                 <C>             <C>                  <C>            <C>
      May 31         Corporate Express
                     Office Products, Inc.         Henderson, NC      $ 7,882          $    712              1/14          196,946
                                                                       =======              ===                            =======
</TABLE>

      The following unaudited pro forma operating information for the six
      months ended June 30, 2000 and 1999, were prepared as if the 2000 and
      1999 acquisitions and dispositions were consummated as of January 1,
      1999.  This information does not purport to be indicative of what the
      operating results of the Partnership would have been had the
      acquisitions and dispositions been consummated on that date.  Pro forma
      amounts are as follows:

<TABLE>
<CAPTION>

                                                                                      Pro Forma
                                                                  (In thousands, except per Unit amounts)
                                                                         Six Months Ended June 30,
                                                                                 2000        1999

<S>                                                                            <C>         <C>
                                              Revenues                         $2,897      $2,771
                                              Expenses                          1,710       1,743
                                                                                -----       -----
                                              Net income                       $1,187      $1,028
                                                                                =====       =====

                                              Net income per Unit of limited
                                               partnership interest            $37.80      $32.74
                                                                                =====       =====
</TABLE>

5.    Mortgages and Notes Payable
      ---------------------------

      On May 31, 2000, in connection with the acquisition of a property
      located in Henderson, North Carolina, the Partnership assumed
      approximately $4.68 million of first mortgage financing.  The note
      bears interest at 7.39% per annum and matures on May 1, 2009.  The note
      requires annual debt service payments of principal and interest of
      approximately $417,000 with a balloon payment of approximately $3.85
      million at maturity.  The Partnership issued a demand note of
      approximately $3.07 million to Lexington Corporate Properties Trust,
      whose chairman and Co-Chief Executive Officer is an officer and a
      shareholder of the General Partner.  The note bears interest at 10% per
      annum with interest only payments and was fully paid in July 2000.



<PAGE>   7

                    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).  For the six months ended
      June 30, 2000 and 1999, property management fees of $24,000 and $18,000
      were incurred.

      Lexington Corporate Properties Trust ("Lexington"), whose chairman and
      Co-Chief Executive Officer is an officer and a shareholder of the
      General Partner, is reimbursed by the Partnership for various
      administrative services performed.  For the six months ended June 30,
      2000 and 1999 such reimbursements totaled $77,000 and $85,000,
      respectively.

      On May 31, 2000, the Partnership purchased from Lexington a property
      located in Henderson, North Carolina for approximately $7.9 million net
      leased to Corporate Express Office Products, Inc.




<PAGE>   8

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


Liquidity and Capital Resources
-------------------------------

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 of
the Partnership could be adversely affected by unanticipated costs, lessees
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.

The unpaid cumulative preferred return at June 30, 2000 totaled $15.469
million ($499.47 to $505.32 per Unit, per close), and was reduced by $384,958
($12.51 per Unit) with the distribution paid in July 2000.

On May 31, 2000, in connection with the acquisition of a property located in
Henderson, North Carolina, the Partnership assumed approximately $4.68
million of first mortgage financing.  The note bears interest at 7.39% per
annum and matures on May 1, 2009.  The note requires annual debt service
payments of principal and interest of approximately $417,000 with a balloon
payment of approximately $3.85 million at maturity.  The Partnership issued a
demand note of approximately $3.07 million.  The note bears interest at 10%
per annum with interest only payments and was fully paid in July 2000.

The Henderson, North Carolina property was purchased from Lexington Corporate
Properties Trust, whose chairman and Co-Chief Executive Officer is an officer
and a shareholder of the General Partner.

Except for the debt service requirements under the mortgages, there are no
material restrictions upon the Partnership's present or future ability to
make distributions in accordance with the provisions of its Partnership
Agreement.

As of June 30, 2000, the restricted cash represents remaining proceeds from
the sale of properties under the Internal Revenue Code Section 1031,
restricted for payment on the demand note.



<PAGE>   9



Results of Operations (in thousands):
-------------------------------------
<TABLE>
<CAPTION>
                                                                                         Increase (Decrease)
                                       Three months           Six months           Three months          Six months
                                       ended June 30,        ended June 30,            ended                ended
                                       2000     1999          2000     1999        June 30, 2000        June 30, 1999
                                       ----     ----          ----     ----        -------------        -------------

<S>                                   <C>      <C>           <C>       <C>             <C>                  <C>
Total revenues                        $1,083   $ 721         $2,564    $1,868          $  362               $  696
                                       -----     ---          -----     -----             ---                  ---

Total expenses
 Interest                                416     120            750       242             296                  508
 Depreciation and amortization           224      93            424       211             131                  213
 General, administrative
 and other                                80     113            183       232             (33)                 (49)
                                        ----     ---           -----     -----            ----                  ---
                                         720     326          l,357       685             394                  672
                                         ---     ---           -----     -----            ---                  ---
Income before gain on
 sale of properties                    $ 363   $ 395         $1,207    $1,183          $   32               $   24
                                         ===     ===          =====     =====             ===                  ===
</TABLE>

The change in results of operations with respect to revenues, interest and
depreciation for the three and six months ended June 30, 2000, are primarily
attributable to the acquisition and operation of the real property
investments acquired in September 1999 and May 2000.

General and administrative expenses decreased in the three and six months ended
June 30, 2000 due to property appraisals performed on all properties in the
first quarter of 1999.



                ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES
                                ABOUT MARKET RISK


There is no exposure to market risk since all of the Partnership's long-term
indebtedness is fixed rate.




<PAGE>   10

                           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 second quarter ended
                  June 30, 2000.

                  None.


<PAGE>   11


                                   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:  August 11, 2000                       By: /s/ E. Robert Roskind
      ------------------------------             ----------------------------
                                                 E. Robert Roskind
                                                 President