<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, 2001

                                       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 000-22596


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


<TABLE>
<S>                                                  <C>
                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
</TABLE>


<TABLE>
<S>                                                          <C>
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
</TABLE>

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 SUBSIDIARIES

                     CONDENSED CONSOLIDATED BALANCE SHEETS
                 (Dollars in thousands, except per Unit amounts)

                 June 30, 2001 (Unaudited) and December 31, 2000



<TABLE>
<CAPTION>
                                                       June 30,     December 31,
                  Assets                                 2001          2000
                                                       --------      --------

<S>                                                    <C>           <C>
Real estate, at cost                                   $ 47,273      $ 47,273
  Less: accumulated depreciation                          3,924         3,421
                                                       --------      --------
                                                         43,349        43,852

Cash and cash equivalents                                 1,045           782
Deferred expenses (net of accumulated amortization
  of $6 and $3 in 2001 and 2000, respectively)               44            47
Rent receivable                                             828           722
Other assets                                                649           952
                                                       --------      --------

                                                       $ 45,915      $ 46,355
                                                       ========      ========


     Liabilities and Partners' Capital

Mortgages and notes payable                            $ 18,659      $ 19,060
Unsecured note                                            1,380         1,326
Accrued interest payable                                     73            89
Accounts payable and other liabilities                    1,630         2,258
                                                       --------      --------
                                                         21,742        22,733

Partners' capital (deficit):
General Partner                                             (86)          (97)
Limited Partners ($1,000 per Unit, 50,000 Units
  authorized, 30,772 Units issued and outstanding)       24,259        23,719
                                                       --------      --------
   Total partners' capital                               24,173        23,622
                                                       --------      --------

                                                       $ 45,915      $ 46,355
                                                       ========      ========
</TABLE>


     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   3
                           NET 1 L.P. AND SUBSIDIARIES

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

                Three and Six Months Ended June 30, 2001 and 2000
                                   (Unaudited)



<TABLE>
<CAPTION>
                                         Three Months Ended         Six Months Ended
                                              June 30,                 June 30,
                                          2001         2000         2001         2000
                                        ------       ------       ------       ------
<S>                                     <C>          <C>          <C>          <C>
Revenues:
  Rental                                $1,157       $1,022       $2,863       $2,462
  Interest and other                        19           61           37          102
                                        ------       ------       ------       ------
                                         1,176        1,083        2,900        2,564
                                        ------       ------       ------       ------
Expenses:
  Interest expense                         403          416          810          750
  Depreciation and amortization            253          224          506          424
  General, administrative and other        126           80          247          183
                                        ------       ------       ------       ------

                                           782          720        1,563        1,357
                                        ------       ------       ------       ------

Net income                              $  394       $  363       $1,337       $1,207
                                        ======       ======       ======       ======

Net income per Unit of limited
  partnership interest (*)              $12.05 to    $11.05 to    $40.77 to    $36.67 to
                                        =========    =========    =========    =========
                                        $12.88       $11.87       $43.72       $39.49
                                        ======       ======       ======       ======
</TABLE>


(*)  Amounts allocated to unit holders vary depending on the dates they became
     unit holders.


     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   4
                           NET 1 L.P. AND SUBSIDIARIES

                 CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
                             (Dollars in thousands)

                     Six Months Ended June 30, 2001 and 2000
                                   (Unaudited)



<TABLE>
<CAPTION>
                                                      2001         2000
                                                     -------      -------

<S>                                                  <C>          <C>
Net cash provided by operating activities            $ 1,450      $ 1,464
                                                     -------      -------

Cash flows from investing activities:
  Investment in real estate                               --         (137)
                                                     -------      -------
  Net cash used in investing activities                   --         (137)
                                                     -------      -------

Cash flows from financing activities:
  Principal payments on mortgage notes                  (401)        (321)
  Increase in deferred expenses                           --          (50)
  Cash distributions to partners                        (786)        (786)
                                                     -------      -------
  Net cash used in financing activities               (1,187)      (1,157)
                                                     -------      -------

Change in cash and cash equivalents                      263          170
Cash and cash equivalents at beginning of period         782        1,951
                                                     -------      -------
Cash and cash equivalents at end of period           $ 1,045      $ 2,121
                                                     =======      =======
</TABLE>


     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   5
                           NET 1 L.P. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
          (Unaudited and dollars in thousands, except per Unit amounts)


                                  June 30, 2001
                                   (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, 2001,
      the Partnership had owned interests in nine properties.

      As of June 30, 2001, the Partnership has a total of 30,772 Units issued
      and outstanding held by 1,341 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,
      2000.

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 the income
      attributable for that period to the Limited Partners. The weighted average
      number of Units outstanding was 30,772 for all periods presented.

      The Financial Accounting Standards Board issued Statement of Financial
      Accounting Standards ("SFAS") No. 133 (Accounting for Derivative
      Instruments and Hedging Activities) which establishes accounting and
      reporting standards for derivative instruments. SFAS 133 requires that an
      entity recognizes all derivatives as either assets or liabilities in the
      balance sheet and measure those instruments at fair value. The
      Partnership's adoption of SFAS 133 on January 1, 2001 had no impact on its
      financial position or results of operations since it has no derivatives.

      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.
<PAGE>   6
                           NET 1 L.P. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
          (Unaudited and dollars in thousands, except per Unit amounts)



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, 2001 totaled $17,314 ($559.43 to
      $565.28 per Unit, per close). On July 31, 2001, the unpaid cumulative
      preferred return was reduced by a cash distribution to the Limited
      Partners totaling $385 ($12.51 per Unit). The General Partner received a
      cash distribution of $8 in July 2001.

4.    Leases

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

      Each of the following tenants/guarantors accounted for 10% or more of
      rental revenues shown for the six months ended June 30, 2001 and 2000:

<TABLE>
<CAPTION>

           Tenants/Guarantors                                     2001     2000
           ------------------                                    ------   ------
<S>                                                              <C>      <C>
        Wal-Mart Stores, Inc. (*)                                  34%     37%
        Bull HN Information Systems, Inc./Bull                     18%     21%
        Cymer, Inc.                                                15%     18%
        Corporate Express Office Products, Inc./Buhrmann NV        14%      3%
        Bally Total Fitness Holding Corporation                    13%     15%
</TABLE>

(*)  Consists of three retail stores located in Gainesville, Georgia, Sumter,
     South Carolina and Brownsville, Texas

Each of the tenants/guarantors which represented 10% or greater of rental
revenue for the six months ended June 30, 2001 and 2000, is a United States
publicly registered company, except for Bull HN Information Systems, Inc. and
Corporate Express Office Products, Inc. Accordingly, each of these companies
files periodic reports with the Securities and Exchange Commission.
<PAGE>   7

                           NET 1 L.P. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
          (Unaudited and dollars in thousands, except per Unit amounts)



4.  Continued

    Summarized financial information, as of and for the year ended December 31,
    2000 for Bull HN Information Systems, Inc. and, as of and for the six
    months ended June 30, 2001 for Corporate Express Office Products, Inc.,
    follows:

<TABLE>
<S>                                                      <C>
Bull HN Information Systems, Inc./BULL:

Current assets                                           $ 1,360,000
Non-current assets                                           540,000
Current liabilities                                        1,227,000
Non-current liabilities                                      589,000
Redeemable preferred stock                                        --
Minority interest                                              6,000

Net sales                                                $ 2,910,000
Gross profit                                                 684,000
Income (loss) - continuing operations                        (92,000)
Net income (loss)                                           (218,000)

Corporate Express Office Products, Inc./Buhrmann NV:

Current assets                                           $ 2,824,000
Non-current assets                                         3,538,000
Current liabilities                                        1,699,000
Non-current liabilities                                    2,391,000
Redeemable preferred stock                                        --
Minority interest                                             29,000

Net sales                                                $ 4,348,000
Gross profit                                                 998,000
Income - continuing operations                                37,000
Net income                                                    11,000
</TABLE>
<PAGE>   8
                           NET 1 L.P. AND SUBSIDIARIES
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
          (Unaudited and dollars in thousands, except per Unit amounts)



5.    Related Party Transactions

      The General Partner has granted Lexington Corporate Properties Trust
      ("Lexington"), whose chairman and Co-Chief Executive Officer is an officer
      and a shareholder of the General Partner, an option exercisable at any
      time, to acquire the general partnership interest. Under the terms of the
      option, Lexington, subject to the approval of any such transaction by the
      independent members of its Board of Trustees, may acquire the general
      partnership interest at its fair market value based upon a formula
      relating to partnership cash flows, with Lexington retaining the option of
      paying such market value in securities of Lexington, limited partnership
      Units in controlled subsidiaries, cash or a combination thereof.

      On November 13, 2000, the Partnership entered into an Agreement and Plan
      of Merger ("Agreement") with Lexington. On July 20, 2001, the Partnership
      announced amended terms of the agreement with Lexington. Under the new
      proposal, Lexington would issue $29,500 in cash and securities, and would
      assume existing debt of the Partnership. The limited partners would
      receive 99% of the merger consideration, payable 50% in cash and 50% in
      Lexington's common shares issued at a value not less than $14.00 per share
      nor more than $16 per share. The General Partner would receive 1% of the
      merger consideration in operating partnership units that are convertible
      into common shares on a one-for-one basis after five years and that would
      receive the same dividend as holders of common shares receive. The
      transaction is subject to customary conditions, including approval by
      Lexington's shareholders and the Partnership's limited partners. As of
      June 30, 2001, Lexington owns 540 units.

      An affiliate of Lexington 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 three and
      six months ended June 30, 2001 and 2000, property management fees of $11
      and $10, and $28 and $24, respectively, were incurred.

      Lexington is reimbursed by the Partnership for various administrative
      services performed. For the three and six months ended June 30, 2001 and
      2000 such reimbursements totaled $47 and $17, and $121 and $77,
      respectively.
<PAGE>   9
                  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, 2001 totaled $17.31 million
($559.43 to $565.28 per Unit, per close), and was reduced by $384,958 ($12.51
per Unit) with the distribution paid in July 2001.

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.

Net cash used in financing activities for each of the six-month periods ended
June 30, 2001 and 2000 totaled $1.19 million and $1.16 million, respectively.
Cash used in financing activities was primarily attributable to cash
distributions to partners and debt service payments.

On November 13, 2000, the Partnership entered into the Agreement with Lexington.
On July 20, 2001, the Partnership announced amended terms of the agreement with
Lexington. Under the new proposal, Lexington would issue $29.5 million in cash
and securities, and would assume existing debt of the Partnership. The limited
partners would receive 99% of the merger consideration, payable 50% in cash and
50% in Lexington's common shares issued at a value not less than $14.00 per
share nor more than $16 per share. The General Partner would receive 1% of the
merger consideration in operating partnership units that are convertible into
common shares on a one-for-one basis after five years and that would receive the
same dividend as holders of common shares receive. The transaction is subject to
customary conditions, including approval by Lexington's shareholders and the
Partnership's limited partners. As of June 30, 2001, Lexington owns 540 units.
<PAGE>   10
Results of Operations (in thousands)

<TABLE>
<CAPTION>


                                    Three months            Six months
                                    ended June 30,         ended June 30,       Increase (Decrease)
                                    2001       2000       2001       2000    Three Months    Six Months
                                    ----       ----       ----       ----   -------------  -------------

<S>                                <C>        <C>        <C>        <C>     <C>            <C>
Total revenues                     $1,176     $1,083     $2,900     $2,564     $   93         $  336
                                   ------     ------     ------     ------     ------         ------

Total expenses
 Interest                             403        416        810        750        (13)            60
 Depreciation and amortization        253        224        506        424         29             82
 General, administrative
  and other                           126         80        247        183         46             64
                                   ------     ------     ------     ------     ------         ------
                                      782        720      l,563      l,357         62            206
                                   ------     ------     ------     ------     ------         ------

Net income                         $  394     $  363     $1,337     $1,207     $   31         $  130
                                   ======     ======     ======     ======     ======         ======
</TABLE>

Total revenues increased in the six months, due to percentage rent received in
the first quarter of 2001.

Interest and depreciation expenses increased in the six months, primarily due to
a full period of interest on the loan and regarding ownership of the Henderson,
North Carolina property.

General and administrative expenses increased in the three and six months,
primarily due to an increase in operating cash.


ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

There is no exposure to market risk since all of the Partnership's mortgages and
notes payable is fixed rate.
<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

                                          None.

            (b)   Reports on Form 8-K filed during the second quarter ended June
                  30, 2001.

                  Form 10-K405/A filed on June 15, 2001. The amendment was filed
                  for the sole purpose of correcting the inadvertent omission of
                  the conformed signature of the Registrant's accountants, KPMG
                  LLP, from the Independent Auditors' Report that is included in
                  Item 8 of the Form 10-K.
<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:  August 14, 2001                     By:  /s/E. Robert Roskind
      ------------------------------              -------------------------
                                                  E. Robert Roskind
                                                  President