<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, 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)

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

<TABLE>
<CAPTION>
                                                           September 30,         December 31,
                                                              1999                  1998
                                                              ----                  ----
                                 Assets
<S>                                                        <C>                  <C>
Real estate, at cost                                        $ 39,837              $ 26,440
   Less:  accumulated depreciation                             2,459                 3,211
                                                            --------              --------
                                                              37,378                23,229

Cash and cash equivalents                                      1,894                 1,688
Rent receivable                                                  459                   455
Other assets                                                      16                   162
                                                            --------              --------

                                                            $ 39,747              $ 25,534
                                                            ========              ========



                    Liabilities and Partners' Capital

Mortgage notes payable                                      $ 16,433              $  5,344
Accrued interest payable                                          27                    28
Accounts payable and other liabilities                           284                   128
                                                            --------              --------
                                                              16,744                 5,500
                                                            --------              --------

Partners' capital (deficit):

General Partner                                                 (110)                 (169)
Limited Partners ($1,000 per Unit, 50,000 Units
   authorized, 30,772 Units issued and outstanding)           23,113                20,203
                                                            --------              --------
                                                              23,003                20,034
                                                            --------              --------

                                                            $ 39,747              $ 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)

             Three and Nine Months Ended September 30, 1999 and 1998
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                    Three Months Ended                   Nine Months Ended
                                                       September 30,                       September 30,
                                                   1999            1998               1999              1998
                                                   ----            ----               ----              ----

<S>                                            <C>            <C>                 <C>                <C>
Revenues:
   Rental                                       $    524       $     702            $   2,353        $   2,491
   Interest and other                                 81              21                  120               60
                                                    ----            ----               ------          -------
                                                     605             723                2,473            2,551
                                                     ---             ---                -----            -----
Expenses:
   Interest expense                                  118             127                  360              386
   Depreciation                                       96             118                  307              355
   General and administrative                         94              77                  326              260
                                                    ----            ----               ------           ------
                                                     308             322                  993            1,001
                                                     ---             ---               ------            -----
Income before gain on sale
   of properties                                     297             401                1,480            1,550
   Gain on sale of properties                         -               -                 2,668               -
                                                   -----          ------                -----            -----

Net income                                      $    297       $     401            $   4,148        $   1,550
                                                     ===             ===                =====            =====

Net income per Unit of limited
   partnership interest                         $   9.45       $   12.77            $  132.10        $   49.36
                                                    ====           =====               ======            =====
</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)

                  Nine Months Ended September 30, 1999 and 1998
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                                     1999                       1998
                                                                                     ----                       ----
<S>                                                                                 <C>                     <C>
Net cash provided by operating activities                                            $ 2,084                   $ 1,777
                                                                                     -------                   -------

Cash flows from investing activities:
   Proceeds from sale of properties, net                                               8,588                         -
   Acquisition of properties, net of mortgage
     liabilities assumed and issued                                                   (9,015)                        -
                                                                                     -------                   -------
   Net cash used in investing activities                                                (427)                        -
                                                                                     -------                   -------

Cash flows from financing activities:

   Principal payments on mortgage notes                                                 (272)                     (246)
   Cash distributions to partners                                                     (1,179)                   (1,179)
                                                                                     -------                   -------
   Net cash used in financing activities                                              (1,451)                   (1,425)
                                                                                     -------                   -------

Change in cash and cash equivalents                                                      206                       352
Cash and cash equivalents at beginning of period                                       1,688                     1,312
                                                                                     -------                   -------
Cash and cash equivalents at end of period                                           $ 1,894                   $ 1,664
                                                                                     =======                   =======

Supplemental disclosure of cash flow information:
Cash paid during the period for interest                                             $   361                   $   387
                                                                                     =======                   =======
</TABLE>


Supplemental disclosure of non-cash investing and financing activities:
On September 27, 1999, the Partnership assumed approximately $4.6 million of
mortgage financing in connection with the acquisition of the San Diego Property.

On September 29, 1999, the Partnership assumed approximately $5.6 million of
mortgage financing and issued a $1.2 million unsecured note in connection with
the acquisition of the Phoenix Property.

     See accompanying notes to unaudited consolidated financial statements.

<PAGE>   5

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

                               September 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 September 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 present 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.

         Certain amounts included in the prior year's financial statements have
         been reclassified to conform to the current year's 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 September 30, 1999 totaled $14.085
         million ($454.50 to $460.35 per Unit, per close). On October 29, 1999,
         the unpaid cumulative preferred return was reduced by a cash
         distribution to the Limited Partners totaling $384,958 ($12.51 per
         Unit). The General Partner received a cash distribution of $7,856 on
         October 29, 1999.


<PAGE>   6

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS

4.       Properties

         During the nine months ended September 30, 1999, the Partnership
         entered into the following real estate transactions:


<TABLE>
<CAPTION>
                                                                                             Lease         Net
                                                             Capitalized    Annualized    Expiration    Rentable
           Date of                                              Costs        Base Rent       Date        Square
         Acquisition     Tenant               Location        ($000's)       ($000's)    (month/year)     Feet
         -----------     ------               --------        --------       --------    ------------     ----
         <S>             <C>                  <C>             <C>           <C>           <C>         <C>
         September 27    Cymer, Inc.         San Diego, CA    $   8,775           778        12/09       65,755
         September 29    Bull HN Information
                         Systems, Inc.       Phoenix, AZ         11,601           972        10/05      137,058
                                                                 ------        ------                   -------

                                                              $  20,376     $   1,750                   202,813
                                                                 ======         =====                   =======
</TABLE>


         The San Diego Property was purchased through a cash payment of
         approximately $4 million and the assumption of a $4.6 million mortgage
         note. The mortgage note bears interest at a rate of 7.5% per annum,
         with a monthly debt service payment of principal and interest in the
         amount of $34,252. The note matures on January 1, 2011 with a balloon
         payment of approximately $3.4 million.

         The Phoenix Property was purchased through a cash payment of
         approximately $4.8 million, the issuance of a $1.2 million unsecured
         note and the assumption of $5.6 million mortgage note. The mortgage
         note bears interest at a rate of 8.12% per annum, with an annual debt
         service payment of principal and interest in the amount of $621,297.
         The mortgage note matures on October 10, 2005 with a balloon payment of
         approximately $4.2 million. The $1.2 million unsecured note has a term
         of 6 years with interest accruing at 8% per annum, due and payable on
         September 30, 2005.

         The San Diego Property, the Phoenix Property and the $1.2 million
         unsecured note were purchased from Lexington Corporate Properties
         Trust, whose chairman is an officer of the General Partner.

         On June 30, 1999, the Partnership sold for cash, sixteen properties
         (the "AutoZone Properties") to AutoZone, Inc., for net proceeds of
         approximately $8.6 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 Partnership
         realized a gain from the sale of approximately $2.7 million.


<PAGE>   7

                    NET 1 L.P. AND CONSOLIDATED PARTNERSHIPS

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


4.       Continued

         The following unaudited pro forma operating information for the nine
         months ended

         September 30, 1999 and 1998, was prepared as if all acquisitions and
         dispositions 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 acquisitions and dispositions been
         consummated on that date. Pro forma amounts are as follows:


<TABLE>
<CAPTION>
                                                                                   Pro Forma
                                                                     (In thousands, except per Unit amounts)
                                                                         Nine months ended September 30,
                                                                              1999             1998
                                                                              ----             ----
                 <S>                                                     <C>                <C>
                  Revenues                                               $   3,548           $  3,440
                  Expenses                                                   1,968              1,926
                                                                             -----              -----
                  Net income                                             $   1,580           $  1,514
                                                                             =====              =====

                  Net income per Unit of limited
                     partnership interest                                $   50.32           $  48.22
                                                                             =====              =====
</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 nine months ended September 30, 1999
         and 1998, property management fees of $23,000 and $24,000 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. In addition, the San Diego Property, the Phoenix Property and
         the $1.2 million unsecured note were purchased from Lexington Corporate
         Properties Trust.


<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 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 September 30, 1999 totaled $14.085
million ($454.50 to $460.35 per Unit, per close), and was reduced by $384,958
($12.51 per Unit) with the distribution paid in October 1999.

During the nine months ended September 30, 1999, the Partnership entered into
the following real estate transactions:


<TABLE>
<CAPTION>
                                                                                           Lease           Net
                                                         Capitalized    Annualized      Expiration      Rentable
      Date of                                               Costs        Base Rent         Date          Square
    Acquisition   Tenant                Location          ($000's)       ($000's)      (month/year)       Feet
    -----------   ------                --------          --------       --------      ------------       ----
   <S>            <C>                   <C>               <C>            <C>            <C>             <C>
   September 27   Cymer, Inc.           San Diego, CA     $  8,775       $     778         12/09         65,755
   September 29   Bull HN Information
                  Systems, Inc.         Phoenix, AZ         11,601             972         10/05        137,058
                                                            ------          ------                      -------

                                                          $ 20,376       $   1,750                      202,813
                                                            ======           =====                      =======
</TABLE>


The San Diego Property was purchased through a cash payment of approximately $4
million and the assumption of a $4.6 million mortgage note. The mortgage note
bears interest at a rate of 7.5% per annum, with a monthly debt service payment
of principal and interest in the amount of $34,252. The note matures on January
1, 2011 with a balloon payment of approximately $3.4 million.

The Phoenix Property was purchased through a cash payment of approximately $4.8
million, the issuance of a $1.2 million unsecured note and the assumption of
$5.6 million mortgage note. The mortgage note bears interest at a rate of 8.12%
per annum, with an annual debt service payment of principal and interest in the
amount of $621,297. The mortgage note matures on October 10, 2005 with a balloon
payment of approximately $4.2 million. The $1.2 million unsecured note has a
term of 6 years with interest accruing at 8% per annum, due and payable on
September 30, 2005.

The San Diego Property, the Phoenix Property and the $1.2 million unsecured note
were purchased from Lexington Corporate Properties Trust, whose chairman is an
officer of the General Partner.

On June 30, 1999, the Partnership sold for cash, sixteen properties (the
"AutoZone Properties") to AutoZone, Inc., for net proceeds of approximately $8.6
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 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>   9


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
October 10, 2005, 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 has closely monitored the Partnership's entire Year 2000 compliance
function. At this time, the Partnership has not developed and does not
anticipate developing any contingency plans with respect to the Year 2000 issue.


<PAGE>   10


Results of Operations (in thousands):


<TABLE>
<CAPTION>
                                                                                    Increase (Decrease)
                                                                        ----------------------------------------
                           Three months ended      Nine months ended    Three months ended     Nine months ended
                              September 30,          September 30,         September 30,         September 30,
                            1999      1998         1999       1998             1999                  1999
                            ----      ----         ----       ----             ----                  ----
<S>                        <C>       <C>        <C>         <C>              <C>                   <C>
Total revenues             $  605    $  723      $ 2,473    $ 2,551          $  (118)              $   (78)
                              ---       ---        -----      -----             ----                  ----

Total expenses:
 Interest                     118       127          360        386               (9)                  (26)
 Depreciation                  96       118          307        355              (22)                  (48)
 General and administrative    94        77          326        260               17                    66
                             ----      ----       ------     ------            -----                  ----
                              308       322          993      1,001              (14)                   (8)
                              ---       ---       ------      -----            -----                 -----
Income before gain on
 sale of properties           297       401        1,480      1,550              104                   (70)
                              ===       ===        =====      =====             ====                  ====
</TABLE>

The results of operations for the three and nine months ended September 30,
1999, are primarily attributable to the acquisition and operation of the real
property investments acquired from 1988 to 1999.

The decreases in total revenues and depreciation expense for the three and nine
months ended September 30, 1999 resulted from the sale of the Autozone
Properties.

General and administrative expenses increased in the nine months ended September
30, 1999 due to property appraisals performed on properties.


<PAGE>   11


                ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES
                                ABOUT MARKET RISK

     There is no exposure to market risk since all of the Partnership's
long-term indebtedness is fixed rate.


<PAGE>   12


                           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.

<TABLE>
<CAPTION>
                  (a)      Exhibits.
                           Exhibit No.                        Exhibit
                           -----------                        -------
                         <S>                         <C>
                                    27               Financial Data Schedule
</TABLE>

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

                      Form 8-K dated June 30, 1999, filed July 15, 1999.
                      Provided financial data information for certain sale of
                      properties located in Alabama (2), Florida (2), Georgia
                      (1), New Mexico (5) and Texas (6) and pro forma financial
                      information for the Partnership.


<PAGE>   13


                                   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 15, 1999                        By: /s/ E. Robert Roskind
      ----------------------                       ----------------------------
                                                     E. Robert Roskind
                                                     President