<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, 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 1. - FINANCIAL INFORMATION

                          ITEM 1. FINANCIAL STATEMENTS

                    NET 1 L. P. AND CONSOLIDATED PARTNERSHIPS

                           CONSOLIDATED BALANCE SHEETS
                                     ($000)

                March 31, 1998 (Unaudited) and December 31, 1997


<TABLE>
<CAPTION>
                                     ASSETS
                                                     March 31,      December 31,
                                                        1998            1997
                                                      --------        --------
<S>                                                   <C>             <C>     
Real estate, at cost                                  $ 26,440        $ 26,440
   Less:  accumulated depreciation                       2,853           2,735
                                                      --------        --------
                                                        23,587          23,705
                                                                    
Cash and cash equivalents                                1,381           1,312
Rent receivable                                            421             400
Other assets                                               551             246
                                                      --------        --------
                                                                    
                                                      $ 25,940        $ 25,663
                                                      ========        ========
                                                                         
                        LIABILITIES AND PARTNERS' CAPITAL
                                                                         
Mortgage notes payable                                $  5,596        $  5,676
Accrued interest payable                                    30              30
Accounts payable and other liabilities                     148             165
                                                      --------        --------
                                                         5,774           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)                        20,333          19,966
                                                      --------        --------
      Total partners' capital                           20,166          19,792
                                                      --------        --------
                                                                    
                                                      $ 25,940        $ 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 March 31, 1998 and 1997
                                   (Unaudited)

<TABLE>
<CAPTION>
                                             Quarter Ended   Quarter Ended
                                                March 31,       March 31,
                                                  1998            1997
                                                 ------          ------
<S>                                              <C>             <C>   
Revenues:

   Rental                                        $1,086          $  900
   Interest and other                                18              28
                                                 ------          ------
                                                             
                                                  1,104             928
                                                 ------          ------
Expenses:                                                    
                                                             
   Interest                                         131              94
   Depreciation                                     118              98
   General, administrative, and other                88              99
                                                 ------          ------
                                                             
                                                    337             291
                                                 ------          ------
                                                             
Net income                                       $  767          $  637
                                                 ======          ======
                                                             
                                                             
Net income per Unit of limited                               
   partnership interest                          $24.43          $20.29
                                                 ======          ======
</TABLE>


     See accompanying notes to unaudited consolidated financial statements.
<PAGE>   4

                    NET 1 L. P. AND CONSOLIDATED PARTNERSHIPS

                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                                     ($000)

                     Quarters Ended March 31, 1998 and 1997
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                   Quarter Ended   Quarter Ended
                                                      March 31,       March 31,
                                                         1998            1997
                                                       -------         -------
<S>                                                    <C>             <C>    
Cash flows from operating activities:                               
                                                                    
   Net income                                          $   767         $   637
                                                       -------         -------
   Adjustments to reconcile net income to                           
     net cash provided by operating activities:                     
     Depreciation                                          118              98
     Other, net                                           (343)           (231)
                                                       -------         -------
     Total adjustments                                    (225)           (133)
                                                       -------         -------
                                                                    
   Net cash provided by operating activities               542             504
                                                       -------         -------
                                                                    
Cash flows from financing activities:                               
   Principal payments on mortgage notes                    (80)            (36)
   Cash distributions to partners                         (393)           (393)
                                                       -------         -------
   Net cash used in financing activities                  (473)           (429)
                                                       -------         -------
                                                                    
Net increase in cash and cash equivalents                   69              75
Cash and cash equivalents at beginning of period         1,312           2,123
                                                       -------         -------
Cash and cash equivalents at end of period             $ 1,381         $ 2,198
                                                       =======         =======
                                                                    
                                                                    
Cash paid during the period for interest               $   131         $    95
                                                       =======         =======
</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, 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 March 31, 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.

2.    Summary of Significant Accounting Policies

      The leases relating to the properties are operating leases in accordance
      with generally accepted accounting principles. Rental revenue is
      recognized on a straight-line basis over the minimum lease terms. At March
      31, 1998, rent receivable primarily consists of amounts for the excess of
      rental revenues recognized on a straight-line basis over the rents
      collectible under the leases.

      For purposes of the statement of cash flows, the Partnership considers all
      highly liquid instruments to be cash equivalents. The balance sheet
      caption cash and cash equivalents includes $1.3 million of money market
      instruments at March 31, 1998.

      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 the quarters ended March 31,
      1998 and 1997.

      Statement of Financial Accounting Standards No. 128 (SFAS 128) " Earnings
      per Share" is effective for periods ending December 15, 1997. Application
      of SFAS 128 had no effect on the Partnership's net income per unit for the
      quarters ended March 31, 1998 and 1997.

      In June 1997, the Financial Accounting Standards Board issued SFAS 130,
      "Reporting Comprehensive Income" and SFAS 131, "Disclosures about Segments
      of an Enterprise and Related Information." SFAS 130 and 131 are effective
      for fiscal years beginning after December 15, 1997. Reclassification of
      financial statements for earlier periods, provided for comparative
      purposes, is required. The adoption of SFAS 130 and 131 on January 1,
      1998, had no effect on the financial statements of the Partnership.
<PAGE>   6

                    NET 1 L. P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


2.    Continued

      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.

      Certain amounts included in the prior years' financial statements have
      been reclassified to conform with the current years' presentation.

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, 1998 totaled $11.317 million
      ($364.56 to $370.41 per Unit, per close). On April 30, 1998, the unpaid
      cumulative preferred return at March 31, 1998 was reduced by a cash
      distribution to the Limited Partners for the quarter ended March 31, 1998
      totaling $384,958 ($12.51 per Unit). The General Partner received a cash
      distribution of $7,856 on April 30, 1998.

4.    Mortgage Notes Payable

      Principal paydowns of the mortgage notes payable for the succeeding five
      years are as follows ($000):

<TABLE>
<CAPTION>
                   Year Ending
                  December 31,                     Amount
                 ---------------                   ------
                 <S>                               <C>   
                 1998 (9 months)                   $  286
                      1999                            416
                      2000                            459
                      2001                            507
                      2002                            560
                      2003                            620
                                                   ======
</TABLE>
<PAGE>   7

                    NET 1 L. P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

5.    Leases

      Minimum total annual future rental payments receivable under the
      noncancelable operating leases for the properties as of March 31, 1998,
      follow ($000):

<TABLE>
<CAPTION>
                   Year Ending
                  December 31,                    Amount
                 ---------------                ---------
                 <S>                            <C>      
                 1998 (9 months)                $   2,073
                      1999                          2,803
                      2000                          2,803
                      2001                          2,804
                      2002                          2,818
                      2003                          2,851
                    2004-2008                      13,160
                      2009                             78
                                                ---------
                                                $  29,390
                                                =========
</TABLE>

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

6.    Related Party Transactions

      Leased Properties Management, Inc., an affiliate of the General Partner,
      is entitled to receive a fee for managing the Partnership's properties in
      the amount of 1% of gross annual rental receipts (or a greater amount in
      certain circumstances). For the quarters ended March 31, 1998 and 1997,
      property management fees of $11,000 and $9,000, respectively had been
      incurred.
<PAGE>   8

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


Liquidity and Capital Resources

The Partnership attempts to maintain a working capital reserve in an amount
equal to 3% of the gross proceeds of its offering, an amount 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, 1998 totaled $11.317 million
($364.56 to $370.41 per Unit, per close), and was reduced by $384,958 ($12.51
per Unit) with the first quarter 1998 distribution paid in April 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.


Results of Operations ($000)

<TABLE>
<CAPTION>
                                     Quarters ended      Increase (Decrease)
                                        March 31,           Quarter ended
                                        ---------           -------------
                                     1998       1997        March 31, 1998
                                     ----       ----        --------------
<S>                                 <C>        <C>              <C>   
Total revenues                      $1,104     $  928           $  176
                                    ------     ------           ------
                                                                
Total expenses:                                                 
   Interest                            131         94               37
   Depreciation                        118         98               20
   General & administrative             88         99              (11)
                                    ------     ------           ------
                                       337        291               46
                                    ------     ------           ------
                                                                
Net income                          $  767     $  637           $  130
                                    ======     ======           ======
</TABLE>
                                                          
The changes in results of operations with respect to revenues, interest and
depreciation for the quarter ended March 31, 1998 are primarily attributable to
the operations of the real property investment acquired in the second quarter of
1997.

General and administrative expenses decreased in the quarter ended March 31,
1998, due to lower property operating expenses.
<PAGE>   9

                           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, 1998. None.
<PAGE>   10

                                   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 13, 1998                    By:/s/ E. Robert Roskind
     ---------------------                   ----------------------------------
                                             E. Robert Roskind
                                             President