<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, 1999
                                       or

[ ]    TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
       EXCHANGE ACT OF 1934
       For the Transition period from                   to
                                      -----------------    ----------------
       Commission File Number 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
                (In thousands, except Units and per Unit amounts)

                 June 30, 1999 (Unaudited) and December 31, 1998


<TABLE>
<CAPTION>
                                                          June 30,    December 31,
                                                            1999          1998
                                                          --------    ------------
<S>                                                       <C>         <C>
                      Assets
                      ------
Real estate, at cost                                      $ 19,461      $ 26,440
   Less:  accumulated depreciation                           2,363         3,211
                                                          --------      --------
                                                            17,098        23,229

Cash and cash equivalents                                    1,792         1,688
Restricted cash                                              8,709          --
Rent receivable                                                831           455
Other assets                                                    15           162
                                                          --------      --------

                                                          $ 28,445      $ 25,534
                                                          ========      ========



          Liabilities and Partners' Capital
          ---------------------------------
Mortgage notes payable                                    $  5,165      $  5,344
Accrued interest payable                                        27            28
Accounts payable and other liabilities                         154           128
                                                          --------      --------
                                                             5,346         5,500
                                                          --------      --------

Partners' capital (deficit):
General Partner                                               (108)         (169)
Limited Partners ($1,000 per Unit, 50,000 Units
   authorized, 30,772 Units issued and outstanding)         23,207        20,203
                                                          --------      --------
     Total partners' capital                                23,099        20,034
                                                          --------      --------

                                                          $ 28,445      $ 25,534
                                                          ========      ========
</TABLE>


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

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

                Three and Six Months Ended June 30, 1999 and 1998
                                   (Unaudited)


<TABLE>
<CAPTION>
                                           Three Months Ended         Six Months Ended
                                                 June 30,                 June 30,
                                            1999         1998         1999         1998
                                            ----         ----         ----         ----
<S>                                        <C>          <C>          <C>          <C>
Revenues:
   Rental                                  $  702       $  703       $1,829       $1,789
   Interest and other                          19           21           39           39
                                           ------       ------       ------       ------
                                              721          724        1,868        1,828
                                           ------       ------       ------       ------
Expenses:
   Interest expense                           120          128          242          259
   Depreciation                                93          119          211          237
   General, administrative and other          113           95          232          183
                                           ------       ------       ------       ------
                                              326          342          685          679
                                           ------       ------       ------       ------
Income before gain on sale
   of properties                              395          382        1,183        1,149
Gain on sale of properties                  2,668         --          2,668         --
                                           ------       ------       ------       ------

Net income                                 $3,063       $  382       $3,851       $1,149
                                           ======       ======       ======       ======

Net income per Unit of limited
   partnership interest                    $97.55       $12.16       $122.65      $36.59
                                           ======       ======       ======       ======
</TABLE>


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

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (In thousands)

                     Six Months Ended June 30, 1999 and 1998
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                           1999           1998
                                                           ----           ----
<S>                                                      <C>            <C>
Cash flows from operating activities:
   Net income                                            $ 3,851        $ 1,149
                                                         -------        -------
   Adjustments to reconcile net income to
     net cash provided by operating activities:
     Depreciation                                            211            237
     Gain on sale of properties                           (2,668)          --
     Increase in rent receivable                            (376)           (42)
     Other, net                                              172           (267)
                                                         -------        -------
     Total adjustments                                    (2,661)           (72)
                                                         -------        -------
   Net cash provided by operating activities               1,190          1,077
                                                         -------        -------

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

Cash flows from financing activities:
   Principal payments on mortgage notes                     (179)          (162)
   Cash distributions to partners                           (786)          (786)
                                                         -------        -------
   Net cash used in financing activities                    (965)          (948)
                                                         -------        -------

Change in cash and cash equivalents                          104            129
Cash and cash equivalents at beginning of period           1,688          1,312
                                                         -------        -------
Cash and cash equivalents at end of period               $ 1,792        $ 1,441
                                                         =======        =======

Supplemental disclosure of cash flow information:
Cash paid during the period for interest                 $   243        $   260
                                                         =======        =======
</TABLE>


     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   5
                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                                  June 30, 1999
                                   (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, 1999, 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 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, 1998.

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, 1999 totaled $13.624 million
         ($439.51 to $445.36 per Unit, per close). On July 30, 1999, the unpaid
         cumulative preferred return at June 30, 1999 was reduced by a cash
         distribution to the Limited Partners for the quarter ended June 30,
         1999 totaling $384,958 ($12.51 per Unit). The General Partner received
         a cash distribution of $7,856 on July 30, 1999.
<PAGE>   6
                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



4.       Properties
         ----------
         On June 30, 1999, the Partnership sold for cash, sixteen properties
         (the "AutoZone Properties") to AutoZone, Inc., for approximately $8.75
         million. The AutoZone Properties aggregating 104,600 square feet,
         consist of retail stores located in Alabama (2), Florida (2), Georgia
         (1), New Mexico (5) and Texas (6). The net proceeds received of
         approximately $8.6 million were deposited in an escrow account,
         restricted under the Internal Revenue Code Section 1031 for investment
         in future acquisitions. The Partnership realized a gain from the sale
         of approximately $2.7 million.

         The following unaudited pro forma operating information for the six
         months ended June 30, 1999 and 1998, were prepared as if the sale of
         the Autozone Properties were consummated as of January 1, 1998. The
         information does not purport to be indicative of what the operating
         results of the Partnership would have been had the sale 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,
                                                   1999              1998
                                                  ------            ------
         <S>                                      <C>               <C>
         Revenues                                 $1,502            $1,460
         Expenses                                    660               629
                                                  ------            ------
         Net income                               $  842            $  831
                                                  ======            ======

         Net income per Unit of limited
            partnership interest                  $26.82            $26.46
                                                  ======            ======
         </TABLE>


5.       Related Party Transactions
         --------------------------
         The LCP Group, L.P., 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, 1999 and
         1998, property management fees of $18,000 and $17,000 were incurred.

         During 1999, the Partnership paid Lexington Corporate Properties
         Trust, whose chairman is an officer of the General Partner, brokerage
         fee relating to the sale of the AutoZone Properties of approximately
         $88,000.

<PAGE>   7
                  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, 1999 totaled $13.624 million
($439.51 to $445.36 per Unit, per close), and was reduced by $384,958 ($12.51
per Unit) with the second quarter 1999 distribution paid in July 1999.

On June 30, 1999, the Partnership sold for cash, sixteen properties (the
"AutoZone Properties") to AutoZone, Inc., for approximately $8.75 million. The
AutoZone Properties aggregating 104,600 square feet, consist of retail stores
located in Alabama (2), Florida (2), Georgia (1), New Mexico (5) and Texas (6).
The net proceeds received of approximately $8.6 million were deposited in an
escrow account, restricted under the Internal Revenue Code Section 1031 for
investment in future acquisitions. The Partnership realized a gain from the sale
of approximately $2.7 million.

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.
<PAGE>   8
Impact of Year 2000
-------------------

The Year 2000 compliance issue concerns the inability of computer systems to
accurately calculate, store or use a date after 1999. This could result in a
system failure or miscalculations causing disruptions of operations.
The Year 2000 issue affects virtually all companies and organizations.

The Partnership has been taking the necessary steps to understand the nature and
extent of the work required to make its core information computer systems and
non-information embedded systems Year 2000 compliant. The Partnership has
determined that it will not be necessary to modify, update or replace its
computer hardware and software applications.

The vendor that provides the Partnership's existing general ledger software has
released a compliant version of its product, which the Partnership is currently
using. The cost of the general ledger system did not have a material effect on
the Partnership's financial condition or results of operations. The
Partnership's properties, which have no scheduled lease expirations prior to
November 30, 2006, are subject to net leases and accordingly the Year 2000
compliance of embedded systems (e.g., security, HVAC, fire and elevator systems)
are the responsibility of the tenants. The Partnership has contacted each of its
tenants asking them to identify and evaluate the changes and modifications
necessary to make these systems compliant for Year 2000 processing. The costs
associated with the effect to make the embedded systems Year 2000 compliant are
the tenant's responsibility. However, no assurances can be given that the
properties' embedded systems will be Year 2000 compliant by December 31, 1999.
Compliance costs, if any, incurred by the Partnership would not be significant.

The Partnership is communicating with significant third-party service providers
and vendors with which it does business to determine the efforts being made on
their part for compliance. The Partnership is attempting to receive compliance
certificates from all third parties that have a material impact on the
Partnership's operations, but no assurance can be given with respect to the cost
or timing of such efforts or the potential effects of any failure to comply.

Management will closely monitor the Partnership's entire Year 2000 compliance
function and will develop contingent plans no later than the third quarter of
1999, if necessary.
<PAGE>   9
Results of Operations (in thousands)
------------------------------------

<TABLE>
<CAPTION>
                                                                                          Increase (Decrease)
                                 Three months ended           Six months ended        Three months    Six months
                                      June 30,                    June 30,               ended          ended
                                 1999          1998          1999          1998       June 30,1999   June 30,1999
                                 ----          ----          ----          ----       ------------   ------------
<S>                            <C>           <C>           <C>           <C>          <C>            <C>
Total revenues                 $   721       $   724       $ 1,868       $ 1,828        $    (3)       $    40
                               -------       -------       -------       -------        -------        -------

Total expenses
 Interest                          120           128           242           259             (8)           (17)
 Depreciation                       93           119           211           237            (26)           (26)
 General, administrative
  and other                        113            95           232           183             18             49
                               -------       -------       -------       -------        -------        -------
                                   326           342           685           679            (16)             6
                               -------       -------       -------       -------        -------        -------
Income before gain on
 sale of properties                395           382         1,183         1,149             13             34
                               =======       =======       =======       =======        =======        =======
</TABLE>


The results of operations for the three and six months ended June 30, 1999, are
primarily attributable to the acquisition and operation of the real property
investments acquired from 1988 to 1997 and interests earned on interest-bearing
bank investments.

Total revenues for the three months ended June 30, 1999 decreased due to a
decrease in interest and other income. Interest and other income decreased due
to the termination of a note received from the sale of a property in 1994.
Rental revenue for the three months ended June 30, 1999 did not materially
change from 1998. Total revenues for the six months ended June 30, 1999
increased due to an increase in rental revenue. Rental revenue increased due to
a higher percentage rent earned in 1999 compared to 1998.

Depreciation expenses for the three and six months ended June 30, 1999 decreased
due to the sale of the AutoZone Properties.

General and administrative expenses increased in the three and six months ended
June 30, 1999 due to property appraisals performed on all properties.
<PAGE>   10
                ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES
                ------------------------------------------------
                                ABOUT MARKET RISK
                                -----------------


There are no exposure to market risk since all of the Partnership's long-term
indebtedness are 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
                  -----------                 -------
                      27               Financial Data Schedule

         (b)      Reports on form 8-K filed during the second quarter ended June
                  30, 1999.

                  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: August 16,1999                      By: /s/ E. Robert Roskind
      ----------------------                  ---------------------
                                              E. Robert Roskind
                                              President