<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 March 31, 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 I. - FINANCIAL INFORMATION

                          ITEM 1. FINANCIAL STATEMENTS

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                           CONSOLIDATED BALANCE SHEETS
                (In thousand, except units and per unit amounts)

                March 31, 1999 (Unaudited) and December 31, 1998


<TABLE>
<CAPTION>
                                                           March 31,  December 31,
            Assets                                           1999         1998
            ------                                         --------     --------
<S>                                                        <C>          <C>     
Real estate, at cost                                       $ 19,461     $ 26,440
     Less:  accumulated depreciation                          2,270        3,211
                                                           --------     --------
                                                             17,191       23,229
                                                                      
Properties held for sale                                      5,920         --
Cash and cash equivalents                                     1,596        1,688
Rent receivable                                                 879          455
Other assets                                                    161          162
                                                           --------     --------
                                                                      
                                                           $ 25,747     $ 25,534
                                                           ========     ========
                                                                      
            Liabilities and Partners' Capital
            ---------------------------------                             

Mortgage notes payable                                     $  5,255     $  5,344
Accrued interest payable                                         28           28
Accounts payable and other liabilities                           36          128
                                                           --------     --------
                                                              5,319        5,500
                                                           --------     --------
Partners' capital (deficit):                                          
General Partner                                                (162)        (169)
Limited Partners ($1,000 per Unit,                                    
     50,000 Units authorized, 30,772                                  
     Units issued and outstanding)                           20,590       20,203
                                                           --------     --------
         Total partners' capital                             20,428       20,034
                                                           --------     --------
                                                           $ 25,747     $ 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)

                     Quarters Ended March 31, 1999 and 1998
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                               Quarter Ended
                                                                  March 31,
                                                              1999         1998
                                                             ------       ------
<S>                                                          <C>          <C>
Revenues:
     Rental                                                  $1,127       $1,086
     Interest and other                                          20           18
                                                             ------       ------
                                                              1,147        1,104
                                                             ------       ------
Expenses:
     Interest                                                   122          131
     Depreciation                                               118          118
     General, administrative, and other                         119           88
                                                             ------       ------
                                                                359          337
                                                             ------       ------
Net income                                                   $  788       $  767
                                                             ======       ======

Net income per Unit of limited
     partnership interest                                    $25.10       $24.43
                                                             ======       ======
</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)

                     Quarters Ended March 31, 1999 and 1998
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                              Quarter Ended
                                                                March 31,
                                                            1999         1998
                                                           -------      -------
<S>                                                        <C>          <C>
Cash flows from operating activities:
     Net income                                            $   788      $   767
                                                           -------      -------
     Adjustments to reconcile net income to
       net cash provided by operating activities:
       Depreciation                                            118          118
       Other, net                                             (515)        (343)
                                                           -------      -------
       Total adjustments                                      (397)        (225)
                                                           -------      -------
     Net cash provided by operating activities                 391          542
                                                           -------      -------

Cash flows from financing activities:
     Principal payments on mortgage notes                      (89)         (80)
     Cash distributions to partners                           (394)        (393)
                                                           -------      -------
     Net cash used in financing activities                    (483)        (473)
                                                           -------      -------

Change in cash and cash equivalents                            (92)          69
Cash and cash equivalents at beginning of period             1,688        1,312
                                                           -------      -------
Cash and cash equivalents at end of period                 $ 1,596      $ 1,381
                                                           =======      =======

Cash paid during the period for interest                   $   122      $   131
                                                           =======      =======
</TABLE>

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

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


                                 March 31, 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 real
      estate or interests therein to be net leased to corporations or other
      entities.

      As of March 31, 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.

      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.

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.

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 March 31, 1999 totaled $13.162 million
      ($424.52 to $430.37 per Unit, per close). On April 30, 1999, the unpaid
      cumulative preferred return at March 31, 1999 was reduced by a cash
      distribution to the Limited Partners for the quarter ended March 31, 1999
      totaling $384,958 ($12.51 per Unit). The General Partner received a cash
      distribution of $7,856 on April 30, 1999.
<PAGE>   6
                    NET 1 L. P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


4.    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 each of the quarters ended March 31, 1999 and 1998, 
      property management fees of $11,000 had been incurred.

5.    Subsequent Events
      -----------------

      On April 22, 1999, the Partnership entered into an agreement to sell the
      Autozone Properties to an unrelated party for a selling price of $8.75
      million. The closing date is expected to occur on or before May 25, 1999.
      The estimated gain on sale of the properties is approximately $2.78
      million.
<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 which 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 March 31, 1999 totaled $13.162 million
($424.52 to $430.37 per Unit, per close), and was reduced by $384,958 ($12.51
per Unit) with the first quarter 1999 distribution paid in April 1999.

On April 22, 1999, the Partnership entered into an agreement to sell the
Autozone Properties to an unrelated party for a selling price of $8.75 million.
The closing date is expected to occur on or before May 25, 1999. The estimated
gain on sale of the properties is approximately $2.78 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.

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 cost
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.
<PAGE>   8
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.

Results of Operations ($000)
----------------------------

<TABLE>
<CAPTION>
                                                 Quarters ended        Increase (Decrease)
                                                   March 31,         Quarter ended March 31,
                                               -------------------   -----------------------
                                                1999         1998             1999
                                               ------       ------           ------
<S>                                            <C>          <C>      <C>   
Total revenues                                 $1,147       $1,104           $   43
                                               ------       ------           ------
                                                                          
Total expenses:                                                           
     Interest                                     122          131               (9)
     Depreciation                                 118          118               --
     General & administrative                     119           88               31
                                               ------       ------           ------
                                                  359          337               22
                                               ------       ------           ------
                                                                          
Net income                                     $  788       $  767           $   21
                                               ======       ======           ======
</TABLE>
                                                                      
The results of operations for the three months ended March 31, 1999, (see
Consolidated Statements of Income) are attributable to the acquisitions and
operation of the real property investments purchased from 1988 to 1997 and
interest earned on interest-bearing bank investments.

Net income for the three months ended March 31, 1999 did not materially change
from 1998.

General and administrative expenses increased in the quarter ended March 31,
1999, due to property appraisals performed on all properties.
<PAGE>   9
                ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES
                ------------------------------------------------
                              ABOUT MARKET RISK
                              -----------------

There are no exposure to market risk due to the Partnership's fixed rate
long-term indebtedness.
<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 first quarter ended March
               31, 1999. 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: May 14, 1999                      By: /s/ E. Robert Roskind
                                            ------------------------
                                            E. Robert Roskind
                                            President