<PAGE>   1





                                                                 EXHIBIT 10.9.2


                              SECOND AMENDMENT TO
                        TWO BRIDGEPOINT LEASE AGREEMENT

             This SECOND AMENDMENT TO TWO BRIDGEPOINT LEASE AGREEMENT (the
"Second Amendment") is entered into as of October 13, 1997, by and between
INVESTORS LIFE INSURANCE COMPANY OF NORTH AMERICA, a Washington corporation
("Landlord"), and BRIGHAM OIL & GAS, L.P., a Delaware limited partnership
("Tenant").

                                R E C I T A L S:

      1.      Landlord and Tenant executed that certain Two Bridgepoint Lease
Agreement ("Original Lease") dated as of September 20, 1996, covering part of
the building (the "Building") known as Two Bridgepoint, located at 6300
Bridgepoint Parkway, Austin, Travis County, Texas, as more particularly
described therein.  Landlord and Tenant executed that certain Amendment to Two
Bridgepoint Lease Agreement ("First Amendment") dated April 11, 1997, amending
the Original Lease. The Original Lease and the First Amendment are hereinafter
collectively referred to as the "Lease". Capitalized terms used in this Second
Amendment and not otherwise defined herein shall have the meanings given to
them in the Lease, unless amended herein.

      2.     Landlord and Tenant have had certain disagreements regarding the
amount of usable square feet ("Usable Square Feet") contained in the Premises,
the applicable common area factors ("Common Area Factors") used to determine
the amount of rentable square feet ("Rentable Square Feet") contained in the
Premises, the actual amount of Rentable Square Feet contained in the Premises,
and the amount of the Additional Tenant Improvement Allowance. Landlord and
Tenant have reached agreement on these matters and such agreement is reflected
in this Second Amendment.

      3.     Landlord and Tenant wish to modify and amend the Lease in order
to, among other things, (i) confirm the amount of Usable Square Feet contained
in the Premises, (ii) confirm the Common Area Factors to be applied in the
Building to convert "usable" space to "rentable" space, (iii) confirm the amount
Rentable Square Feet in the Premises, (iv) confirm that the Premises includes
the entire fifth floor of the Building and the portion of the fourth floor shown
on Exhibit "A" to the First Amendment and designated as the "Initial Area of the
Lease" and the "1st Option Space", (v) confirm the amount of Usable Square Feet
and Rentable Square Feet contained in the 2nd Option Space and the 3rd Option
Space as described on Exhibit "A" to the First Amendment, (vi) to attach a
revised Exhibit "A" to the Lease, (vi) confirm the execution of the Commencement
Date Declaration, (vii) confirm the amount of the Additional Tenant Improvement
Allowance that will be amortized over the Term of the Lease, (viii) confirm the
revised Base Rent based on the amortization of the Additional Tenant Improvement
Allowance, and (ix) confirm Landlord's grant to Tenant of an additional sixty
(60) day option, effective as of the date of this Second Amendment, to exercise
its Expansion Option for up to 6,000 Rentable Square Feet out of the 2nd Option
Space and the 3rd Option Space, but specifically excluding the portion of the
2nd Option Space that Landlord has agreed to lease to Amherst Securities.
<PAGE>   2
      NOW, THEREFORE, in consideration of the above recitals and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, Landlord and Tenant agree to amend the Lease as follows:

      1.     Premises: The Floor Plans attached as Exhibit "A" to the Original
Lease, and the Fourth Floor Plan attached as Exhibit "A" to First Amendment are
hereby deleted and in lieu thereof are inserted the Floor Plans for the fourth
and fifth floors attached to this Second Amendment as Exhibits "A-1 and "A-2".
Landlord and Tenant agree that Premises include the entire fifth floor of the
Building (as shown on Exhibit "A-1") and the portion of the fourth floor of the
Building designated as the "Initial Area of Lease" and the "1st Option Space"
(as shown on Exhibit "A-2").

      2.     Usable Square Feet; Common Area Factors; and Rentable Square Feet.
Landlord and Tenant agree that the Usable Square Feet contained in the Premises
is 27,284, with 19,089 on the fifth floor of the Building and 8,195 on the
fourth floor of the Building. Landlord and Tenant agree that the Common Area
Factor attributable to a single tenant floor in the Building is 1.0556 and the
Common Area Factor for a multi-tenant floor in the Building is 1.1568.
Landlord and Tenant agree that the Common Area Factor is applied to the Usable
Square Feet in the Premises to determine the Rentable Square Feet in the
Premises. The calculation of Rentable Square Feet in the Premises is as
follows:

<TABLE>
<CAPTION>
      Floor                Usable               Common        Rentable
      -----                ------               ------        --------
                         Square Feet          Area Factor    Square Feet
                         -----------          -----------    -----------
      <S>                  <C>           <C>    <C>           <C>
      5th (full floor)     19,089        x      1.0556        20,151
      4th (multi-tenant)    8,195        x      1.1568         9,480
                         -----------                         -----------
      Premises             27,284                             29,631
</TABLE>

Therefore, Landlord and Tenant agree that the Rentable Square Feet contained in
the Premises is 29,631 square feet.

      Landlord and Tenant acknowledge and agree that the calculation of Usable
Square Feet and Rentable Square Feet on multi-tenant floors in the Building is
different from single tenant floors in the Building. As long as the fourth
floor is multi-tenant floor, Landlord and Tenant agree that the usable square
feet contained in the 2nd option space is 4,615 square feet and the Usable
Square Feet contained in the 3rd Option Space is 4,324 square feet. As long the
fourth floor is a multi-tenant floor, Landlord and Tenant agree that the Common
Area Factor applied to Usable Square Feet is 1.1568. Therefore, as long as the
fourth floor is multi-tenant floor, Landlord and Tenant agree that the Rentable
Square Feet contained in the 2nd Option Space is 5,338 (4,615 x 1.1568) and the
Rentable Square Feet contained in the 3rd Option Space is 5,002 (4,324 x
1.1568). If Tenant occupies a portion of the 2nd Option Space or a portion of
the 3rd Option Space, the determination of Usable Square Feet shall be measured
in accordance with the most recent BOMA Standard Method of Floor Measurement
(the "BOMA Standard"), which will be confirmed by Landlord's architect and
Tenants architect, and the multi-tenant Common Area Factor of 1.1568 shall be
applied to such determination of Usable Square Feet.





                                      -2-
<PAGE>   3
      At such time as Tenant occupies the entire fourth floor, the Usable
Square Feet for the fourth floor will be calculated as a single tenant floor
instead of a multi-tenant floor. The Usable Square Feet for the fourth floor as
a single tenant floor is 18,833. The Common Area Factor for a single tenant
floor in the Building is 1.0556. Therefore, if Tenant occupies the entire
fourth floor as a single tenant floor, Landlord and Tenant agree that the
Rentable Square Feet contained in the fourth floor is 19,880 (18,833 x 1.0556).

      3.     Commencement Date Declaration. Tenant has executed and delivered
to Landlord the Commencement Date Declaration, a copy of which is attached
hereto as Exhibit "B" and made a part hereof for all purposes.

      4.     Additional Tenant Improvement Allowance. Landlord and Tenant
acknowledge and agree that the total amount of the Additional Tenant
Improvement Allowance, as described in Section 5 of Exhibit "C" of the Original
Lease, is $256,450.00, and that such amount, plus interest thereon at the rate
of ten percent (10%) per annum, shall be added to the Base Rent and amortized
over the Term of the Lease. Therefore, the Base Rent shall be increased by
$3,389.00 per month to amortize the Additional Tenant Improvement Allowance.

      5.     Base Rent. The monthly Base Rent for the Premises (excluding the 
2nd Option Space and the 3rd Option Space) for Lease Years one (1) through (5)
is $60,181.00 which amount constitutes $56,792.00 monthly Base Rent for the
29,631 Rentable Square Feet, plus $3,389.00 additional monthly Base Rent
resulting from the amortized Additional Tenant Improvement Allowance. The
monthly Base Rent for the Premises (excluding the 2nd Option Space and the 3rd
Option Space) for Lease Years six (6) through (10) is $62,651.00, which amount
constitutes $59,262.00 monthly Base Rent on the 29,631 Rentable Square Feet,
plus $3,389.00 additional monthly Base Rent resulting from the amortized
Additional Tenant Improvement Allowance.

      6.     Expansion Option. Landlord has disclosed to Tenant that Landlord
is currently negotiating a lease with Amherst Securities (the "Amherst
Securities Lease") for approximately 4,000 square feet in the 2nd Option Space,
which space is adjacent to the Premises and is reflected on Exhibit "C"
attached hereto (the "Amherst Premises"). Landlord acknowledges and agrees that
the Amherst Securities Lease will be subject to Tenant's existing Expansion
Option as set Forth in Section 2.05 and Exhibit "G" of the Lease. In Addition
to the Tenant's rights under the Current Expansion Option as set forth in the
Lease, Landlord hereby grants to Tenant, for a period of sixty (60) days from
the date of this Second Amendment, the limited right to exercise Tenant's
Expansion Option for a maximum of 6,000 Rentable Square Feet in the 2nd Option
Space and/or the 3rd Option Space (excluding the Amherst Premises). Except as
set forth in this Section 6 of this Second Amendment, all of the terms and
conditions of Exhibit "G" shall be applicable to Tenant's right to exercises the
Expansion Option on such portions of the 2nd Option Space and/or the 3rd Option
Space. Further, Landlord agrees not to enter into any additional leases related
to the 2nd Option Space or the 3rd Option Space (other than the Amherst
Securities Lease) during this sixty (60) day period. If Tenant elects not to
exercise its right to exercise the Expansion Option during such sixty (60) day
period, Tenant's limited right to exercise the Expansion Option early as set
forth in this Second Amendment shall terminate, but Tenant shall continue to
have all rights to exercise the Expansion Option in accordance with Exhibit "G"
of the Lease at the times set forth therein.





                                      -3-
<PAGE>   4
      7.     Ratification . The Lease, as amended by this Second Amendment, is
hereby ratified and confirmed in all respects.

      8.     Counterparts. This Second Amendment may be executed in one or more
counterparts, each of which when so executed shall be deemed an original. Such
counterparts, together, shall constitute but one and the same instrument.

      IN WITNESS WHEREOF, the parties have executed this Second Amendment as of
the date first above written.

                                        LANDLORD:

                                        INVESTORS LIFE INSURANCE COMPANY OF
                                         NORTH AMERICA, a Washington
                                         corporation


                                        By:  /s/ RAY MITTE
                                           -----------------------------------
                                        Name:   Ray Mitte
                                              --------------------------------
                                        Title:  President
                                              --------------------------------


                                        TENANT:

                                        BRIGHAM OIL & GAS, L.P., a Delaware
                                        limited partnership

                                        By:    Brigham, Inc., a Texas
                                               corporation, as managing
                                               general partner

                                               By:  /s/ BEN M. BRIGHAM
                                                  -----------------------------
                                                    Ben M. Brigham 
                                                    President and CEO





                                      -4-
<PAGE>   5
                                  EXHIBIT "A"

                      TO SECOND AMENDMENT TO LEASE BETWEEN
                        INVESTORS LIFE INSURANCE COMPANY
                         OF NORTH AMERICA, AS LANDLORD,
                     AND BRIGHAM OIL & GAS, L.P., AS TENANT

                                  FLOOR PLANS





<PAGE>   6
                              [FIFTH FLOOR PLAN]





                                 EXHIBIT "A-1"
<PAGE>   7
                             [FOURTH FLOOR PLAN]





                                 EXHIBIT "A-2"
<PAGE>   8
                                  EXHIBIT "B"

                      TO SECOND AMENDMENT TO LEASE BETWEEN
                        INVESTORS LIFE INSURANCE COMPANY
                         OF NORTH AMERICA, AS LANDLORD,
                     AND BRIGHAM OIL & GAS, L.P., AS TENANT

                         COMMENCEMENT DATE DECLARATION
<PAGE>   9
                         COMMENCEMENT DATE DECLARATION

      This declaration is executed with respect to that certain Lease Agreement
(the "Original Lease") dated September 20, 1996 by and between Investors Life
Insurance Company of North America, a Washington corporation ("Landlord"), and
Brigham Oil & Gas, L.P., a Delaware limited partnership ("Tenant"), amended by
that certain First Amendment to Two Bridgepoint Lease Agreement ("First
Amendment) dated April 11, 1997, and further amended by that certain Second
Amendment to Two Bridgepoint Lease Agreement ("Second Amendment") dated
October ___, 1997, covering approximately 29,631 square feet of rentable area on
floors four and five of the Building. The Original Lease, the First Amendment
and the Second Amendment are hereinafter collectively referred to as the
"Lease". Capitalized terms used but not defined herein shall have the meanings
given to them in the Lease.

      By their respective execution below, Landlord and Tenant each hereby
stipulates and agrees that:

      (1)    The Commencement Date (as defined in Section 2.02 of the Lease)
             occurred on July 15, 1997, and the Expiration Date is June 30,
             2007.

      (2)    The portion of the Premises located on the fifth floor of the
             Building contains 20,151 rentable square feet as depicted on
             Exhibit "A" attached hereto and made a part hereof for all
             purposes, intentionally deleting the previous Exhibit "A-3"
             attached to the Lease, and the portion of the Premises located on
             the fourth floor of the Building contains 9,480 rentable square
             feet as depicted on Exhibit "B" attached hereto and made a part
             hereof for all purposes, intentionally deleting the previous
             Exhibit "A-2" attached to the Lease. The space occupied by Tenant
             on the fourth floor of the Building includes the initial area
             contemplated by the Lease, as well as the 1st Option Space as
             described in Exhibit "G" to the Lease.

      (3)    Tenants Percentage Share for purposes of calculating Tenants
             Percentage Share of Operating Expenses in excess of the Expense
             Stop is 32.048%

      (4)    Base Rent, including the amortized Additional Tenant Improvement
             Allowance, is $24.37 per rentable square foot per year for Lease
             Years 1 through 5, payable in equal monthly installments of
             $60,181.00 starting on July 15, 1997 (provided, however, the Base
             Rent for the month of July, 1997 shall be prorated as provided in
             Section 3.01 of the Lease). Base Rent, including the amortized
             Additional Tenant Improvement Allowance, is $25.37 per rentable
             square foot per year for Lease Years 6 through 10, payable in
             equal monthly installments of $62,651.00, starting on July
             1,2001.





                                      1
<PAGE>   10
           (5)    All construction work per the Drawings is complete.

      This declaration may be relied upon by any person having or acquiring an
interest in the Lease or the Building, without notice to or consent of Landlord
or Tenant.

      EXECUTED on this _____ day of October, 1997.

                                  LANDLORD:

                                  INVESTORS LIFE INSURANCE COMPANY OF NORTH
                                  AMERICA, a Washington corporation

                                  By:
                                      ----------------------------------------
                                  Name:
                                        --------------------------------------
                                  Title:
                                        --------------------------------------


                                  TENANT:

                                  BRIGHAM OIL & GAS, L.P., a Delaware limited
                                  partnership

                                  By:    Brigham, Inc., a Texas corporation, as
                                         managing general partner

                                         By:
                                             ----------------------------------
                                                Ben M. Brigham 
                                                President and CEO





                                      2
<PAGE>   11
                                  EXHIBIT "C"

                      TO SECOND AMENDMENT TO LEASE BETWEEN
                        INVESTORS LIFE INSURANCE COMPANY
                         OF NORTH AMERICA, AS LANDLORD,
                     AND BRIGHAM OIL & GAS, L.P., AS TENANT

                                AMHERST PREMISES
<PAGE>   12
                             [FOURTH FLOOR PLAN]





                                 EXHIBIT "C"
<PAGE>   13
                   [BRIGHAM EXPLORATION COMPANY LETTERHEAD]


                                April 7, 1998
                 Via Facsimile Transmission and Hand Delivery

Ms. Trina Willis                               Mr. David M. Lepore
FIC Realty Services          Hand Delivered    M&P Partners Limited Partnership 
6300 Bridge Point Parkway    by Sheri Lancon   400 Centre Street
Bldg. One, Suite 325             4/7/98        Newton, MA 02158
Austin, Texas 78730                            Fax # (617) 332-2261
Fax # (512) 404-5212                         
                         
                         
Ms. Julia D. Finney
Reit Management & Research, Inc.
6300 Bridge Point Parkway, Bldg. One, Suite 125
Austin, Texas 78730
Fax # (512) 346-7561

      Re:    Two Bridge Point Lease Agreement by and between Investors Life
             Insurance Company of North America and Brigham Oil & Gas, L.P.,
             dated September 20, 1996, as amended (the "Lease Agreement");
             EXERCISE OF RIGHT OF FIRST REFUSAL

Ladies and Gentlemen:

      On March 24, 1998 we received Ms. Julia D. Finney's letter dated March
20, 1998, notifying us that the Right of First Refusal Space (the "Refusal
Space") is available for lease and that Health and Retirement Properties Trust
("Landlord") has prospects interested in leasing the Refusal Space.

      Brigham Oil & Gas, L.P. ("Tenant") hereby notifies Landlord that, under
and pursuant to the terms of Section 2.04 and Exhibit F of the Lease Agreement,
Tenant is exercising its Right of First Refusal to lease all of the "3rd Option
Space" as depicted on Exhibit A-2 to the Lease Agreement, being the same space
which is also known as the "5 Year Option Space."

      Tenant is not exercising its Right of First Refusal with respect to the
remainder of the "2nd Option Space" (being all of the 2nd Option Space which has
not already been leased to Amherst).

      Please feel free to give me a call if anything else is needed with
respect to this matter.

                                  Sincerely,
                                  BRIGHAM OIL & GAS, L.P.
                                        By Brigham, Inc.
                                        Its Managing General Partner

                                        /s/ ANNE L. BRIGHAM

                                        Anne L. Brigham       
                                        Executive Vice President

cc: Ms. Diana Barbour, Oxford Commerical, Inc.