<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 September 30, 1998

                                       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
                                     ($000)

              September 30, 1998 (Unaudited) and December 31, 1997



               ASSETS
<TABLE>
<CAPTION>
                                               September 30,     December 31,
                                                   1998              1997
                                               -------------     ------------
<S>                                             <C>              <C>      
Real estate, at cost                             $26,440          $  26,440
Less:  accumulated depreciation                    3,090              2,735
                                                 -------            -------
                                                  23,350             23,705

Cash and cash equivalents                          1,664              1,312
Rent receivable                                      443                400
Other assets                                         284                246
                                                 -------            -------

                                                 $25,741          $  25,663
                                                  ======             ======



           LIABILITIES AND PARTNERS' CAPITAL

Mortgage notes payable                          $  5,430         $   5,676
Accrued interest payable                              29                30
Accounts payable and other liabilities               119               165
                                                 -------            ------
                                                   5,578             5,871
                                                  ------             -----

Partners' capital (deficit):
  General Partner                                   (167)             (174)
  Limited Partners ($1,000 per Unit,
  50,000 Units authorized, 30,772
  Units issued and outstanding)                   20,330            19,966
                                                  ------            ------
  Total partners' capital                         20,163            19,792
                                                  ------            ------

                                                $ 25,741         $  25,663
                                                  ======            ======
</TABLE>





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

                        CONSOLIDATED STATEMENTS OF INCOME
                         ($000 EXCEPT PER UNIT AMOUNTS)

               Quarters Ended September 30, 1998 and 1997 and Nine
                    Months Ended September 30, 1998 and 1997
                                   (Unaudited)



<TABLE>
<CAPTION>
                                                                Nine Months     Nine Months
                               Quarter Ended   Quarter Ended      Ended           Ended
                                September 30,  September 30,   September 30,    September 30,
                                    1998            1997            1998            1997  
                                   ------          ------          ------          ------
                                                                                
<S>                               <C>             <C>              <C>            <C>
Revenues:                                                                       
                                                                                
  Rental                           $  702          $  701          $2,491          $2,250
  Interest and other                   21              17              60              70
                                   ------          ------          ------          ------
                                                                                
                                      723             718           2,551           2,320
                                   ------          ------          ------          ------
                                                                                
Expenses:                                                                       
                                                                                
  Interest expense                    127             134             386             336
  Depreciation                        118             118             355             321
  General, administrative                                                       
  and other                            77              58             260             253
                                   ------          ------          ------          ------
                                                                                
                                      322             310           1,001             910
                                   ------          ------          ------          ------
                                                                                
Net income                         $  401          $  408          $1,550          $1,410
                                   ======          ======          ======          ======
                                                                                
                                                                                
Net income per Unit of limited                                                  
  partnership interest             $12.77          $12.98          $49.36          $44.90
                                   ======          ======          ======          ======
</TABLE>
                                                                                
                                                                           
     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   4
                    NET 1 L. P. AND CONSOLIDATED PARTNERSHIPS

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                     ($000)

                  Nine months ended September 30, 1998 and 1997
                                   (Unaudited)




<TABLE>
<CAPTION>
                                                      Nine Months           Nine Months
                                                         Ended                Ended
                                                    September 30, 1998   September 30, 1997
                                                         -------              -------
                                                                             
<S>                                                 <C>                  <C>  
Cash flows from operating activities:                                        
  Net income                                             $ 1,550              $ 1,410
                                                         -------              -------
  Adjustments to reconcile net income to                                     
     net cash provided by operating activities:                              
     Depreciation                                            355                  321
     Other, net                                             (128)                 (28)
                                                         -------              -------
     Total adjustments                                       227                  293
                                                         -------              -------
                                                                             
  Net cash provided by operating activities                1,777                1,703
                                                         -------              -------
                                                                             
Cash flows from investing activities:                                        
  Acquisition of property, net of                                            
     mortgage liability assumed                               --               (1,204)
                                                         -------              -------
  Net cash used in investing activities                       --               (1,204)
                                                         -------              -------
                                                                             
Cash flows from financing activities:                                        
  Principal payments on mortgage notes                      (246)                (163)
  Cash distributions to partners                          (1,179)              (1,178)
                                                         -------              -------
  Net cash used in financing activities                   (1,425)              (1,341)
                                                         -------              -------
                                                                             
Net increase (decrease) in cash and cash equivalents         352                 (842)
                                                                             
Cash and cash equivalents at beginning of period           1,312                2,123
                                                         -------              -------
                                                                             
Cash and cash equivalents at end of period               $ 1,664              $ 1,281
                                                         =======              =======
                                                                             
Supplemental disclosure of cash flow information:                            
                                                                             
Cash payments for interest                               $   387              $   337
                                                         =======              =======
</TABLE>
                                                                             
                                                                        

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

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


                               September 30, 1998
                                   (Unaudited)



1.    The Partnership and Basis of Presentation

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

      As of September 30, 1998, the Partnership has a total of 30,772 Units
      issued and outstanding held by approximately 1,500 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, 1997.

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

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.

      In June 1997, SFAS No. 130,"Reporting Comprehensive Income", and SFAS No.
      131, "Disclosures about Segments of an Enterprise and Related
      Information," were issued. SFAS No. 130 established standards for
      reporting and displaying comprehensive income and its components in a
      financial statement that is displayed with the same prominence as other
      financial statements. Reclassification of financial statements for earlier
      periods, provided for comparative purposes, is required. The statement
      also requires the accumulated balance of other comprehensive income to be
      displayed separately from retained earnings and additional paid-in capital
      in equity section of the balance sheet. SFAS No. 131 establishes standards
      for reporting information about operating segments in annual and interim
      financial statements.
<PAGE>   6
                    NET 1 L. P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS



2.    Continued

      Operating segments are defined as components of an enterprise about which
      separate financial information is available that is evaluated regularly by
      the chief operating decision maker in deciding how to allocate resources
      and in assessing performance. Categories required to be reported as well
      as reconciled to the financial statements are segment profit or loss,
      certain specific revenue and expense items, and segment assets. SFAS No.
      130 and No. 131 are effective for fiscal years beginning after December
      15, 1997. The adoption of these standards had no impact on the
      Partnership's financial position and operating results as of and for the
      nine months ended September 30, 1998.

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 September 30, 1998 totaled $12.24 million
      ($394.54 to $400.39 per Unit, per close). On October 30, 1998, the unpaid
      cumulative preferred return at September 30, 1998 was reduced by a cash
      distribution to the Limited Partners for the quarter ended September 30,
      1998 totaling $384,958 ($12.51 per Unit). The General Partner received a
      cash distribution of $7,856 on October 30, 1998.

4.    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 nine months ended September 30, 1998 and
      1997, property management fees of $24,000 and $22,000, respectively had
      been incurred.
<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 September 30, 1998 totaled $12.24
million ($394.54 to $400.39 per Unit, per close), and was reduced by $384,958
($12.51 per Unit) with the third quarter 1998 distribution paid in October 1998.

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.

Recent Accounting Pronouncements

In June 1997, SFAS No. 130,"Reporting Comprehensive Income", and SFAS No. 131,
"Disclosures about Segments of an Enterprise and Related Information," were
issued. SFAS No. 130 established standards for reporting and displaying
comprehensive income and its components in a financial statement that is
displayed with the same prominence as other financial statements.
Reclassification of financial statements for earlier periods, provided for
comparative purposes, is required. The statement also requires the accumulated
balance of other comprehensive income to be displayed separately from retained
earnings and additional paid-in capital in equity section of the balance sheet.
SFAS No. 131 establishes standards for reporting information about operating
segments in annual and interim financial statements. Operating segments are
defined as components of an enterprise about which separate financial
information is available that is evaluated regularly by the chief operating
decision maker in deciding how to allocate resources and in assessing
performance. Categories required to be reported as well as reconciled to the
financial statements are segment profit or loss, certain specific revenue and
expense items, and segment assets. SFAS No. 130 and No. 131 are effective for
fiscal years beginning after December 15, 1997. The adoption of these standards
had no impact on the Partnership's financial position and operating results as
of and for the nine months ended September 30, 1998.
<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 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 and
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 if necessary.
<PAGE>   9
Results of Operations ($000)


<TABLE>
<CAPTION>
                                   Quarters                    Nine months          Increase (Decrease)
                                    ended                         ended           Quarters      Nine months
                                September 30,                 September 30,         ended          ended
                              1998          1997          1998          1997     September 30,   September 30,
                              ----          ----          ----          ----     ------------    ------------
<S>                          <C>           <C>           <C>           <C>           <C>            <C>   
Total revenues               $  723        $  718        $2,551        $2,320        $    5         $  231
                             ------        ------        ------        ------        ------         ------
                                                                                                
Total expenses                                                                                  
 Interest                       127           134           386           336            (7)            50
 Depreciation                   118           118           355           321            --             34
 General, administrative                                                                        
  and other                      77            58           260           253            19              7
                             ------        ------        ------        ------        ------         ------
                                322           310         1,001           910            12             91
                             ------        ------        ------        ------        ------         ------
                                                                                                
Net income                   $  401        $  408        $1,550        $1,410        $   (7)        $  140
                             ======        ======        ======        ======        ======         ======
</TABLE>


The results of operations for the quarter ended September 30, 1998 did not   
change significantly from the quarter ended September 30, 1997. The changes in
results of operations with respect to revenues, interest and depreciation for
the nine months ended September 30, 1998, compared to the same period in 1997
are primarily attributable to the operations of the real property investment
acquired in the second quarter of 1997.

Accounting Standards Issued but not yet Adopted

In June, 1998, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 133 ("SFAS 133") "Accounting for Derivative
Instruments and Hedging Activities". The Statement establishes accounting and
reporting standards for derivative instruments and hedging activities. This
Statement is effective for all fiscal quarters of fiscal years beginning after
June 15, 1999. The adoption of SFAS 133 is not expected to have any impact on
the financial position or results of operations of the Partnership.

            ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURES
                               ABOUT MARKET RISK 
            -------------------------------------------------

                             Not applicable.
<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 third quarter ended
                  September 30, 1998.
                  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: November 12, 1998                      By:/s/ E. Robert Roskind   
    -------------------------                  --------------------------------
                                                 E. Robert Roskind
                                                 President