<PAGE>

                                                                     Exhibit 4.2

                          ESPERION THERAPEUTICS, INC.
               AMENDMENT NO. 1 TO THE INVESTOR'S RIGHTS AGREEMENT

     This AMENDMENT NO. 1 TO THE INVESTORS' RIGHTS AGREEMENT (this "Agreement")
is made and entered into as of August 11, 1998, by and among ESPERION
THERAPEUTICS, INC., a Delaware corporation (the "Company"), the Purchasers (as
                                                 -------
such term is defined in the Original Agreement defined below), and the
Additional Purchasers set forth on Exhibit 1 attached hereto under the heading
                                   ---------
"Additional Purchasers".
----------------------

     WHEREAS, the Company and the Purchasers are parties to an Investors' Rights
Agreement made and entered into as of July 6, 1998 (the "Original Agreement");
                                                         ------------------
and

     WHEREAS, the parties to the Original Agreement desire to amend such
agreement to provide for the addition of the Additional Purchasers as Purchasers
thereunder, among other things, on the terms and conditions stated herein and in
the Original Agreement;

     NOW, THEREFORE, in consideration of the mutual promises and covenants set
forth herein, the parties hereto agree as follows:

                1. Defined Terms. Capitalized terms used and not otherwise
                   -------------
defined in this Agreement shall have the meanings given to such terms in the
Original Agreement.

                2. Exhibit A. Exhibit A to the Original Agreement is amended and
                   ---------  ---------
restated in the form of Exhibit A hereto.
                        ---------

                3. Joinder. The Additional Purchasers hereby agree to be bound
                   -------
by and subject to the terms and conditions of the Original Agreement and the
parties hereto agree that the Additional Purchasers shall be entitled to all, of
the rights and benefits of the Purchasers under the Original Agreement.

                4. Amendment to Section 4.3. Section 4.3 of the Original
                   ------------------------
Agreement is hereby amended by adding the following clause immediately prior to
the period at the end of the second sentence of such Section:

     "; provided, however, that without the consent of a Holder, no such
        --------  -------
     amendment shall alter the provisions of Sections 2.1 or 2.2 with respect to
     the Preferred Shares held by such Holder"

                5. Governing Law. This Agreement shall be governed in all
                   -------------
respects by the laws of the State of Delaware, as applied to agreements among
Delaware residents entered into and to be performed entirely within Delaware.

                6. Effective Date. In accordance with the terms of the Original
                   --------------
Agreement, this Agreement will become effective upon execution by the Company
and the holders of at least fifty one percent (51%) of the Preferred Shares.
<PAGE>

                7. Counterparts. This Agreement may be executed in any number of
                   ------------
counterparts. each of which shall be an original, but all of which, together
shall constitute one instrument.


                 *          *          *          *          *
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have executed this Investors' Rights
Agreement effective as of the day and year first above written.


THE COMPANY:                            ESPERION THERAPEUTICS, INC.

                                        By: /s/ Roger S. Newton
                                           --------------------------
                                           Name:  Roger S. Newton
                                           Title: President/CEO


THE PURCHASERS:                         OAK INVESTMENT PARTNERS VII,
                                        LIMITED PARTNERSHIP

                                        By:  OAK ASSOCIATES VII, LLC
                                             Its General Partner

                                        By:  _____________________________
                                             A Member


                                        OAK VII AFFILIATES FUND, LIMITED
                                        PARTNERSHIP

                                        By:  OAK VII AFFILIATES, LLC
                                             Its General Partner

                                        By:  ______________________________
                                             A Member



     [Signature page to Amendment No. 1 to the Investors' Rights Agreement]
<PAGE>

                              TL VENTURES III L.P.

                              By:  TL Ventures III Management L.P.,
                                   its general partner

                              By:  TL Ventures III L.L.C.
                                   its general partner

                              By: /s/ Christopher Moller
                                 ------------------------------------
                                  Name:  Christopher Moller Ph.D.
                                  Title: Managing Director

                              TL VENTURES III OFFSHORE L.P.

                              By:  TL Ventures III Offshore Partners, L.P.,
                                   its general partner

                              By:  TL Ventures III Offshore Ltd,
                                   its general partner

                              By: /s/ Christopher Moller
                                 ------------------------------------
                                  Name:  Christopher Moller Ph.D.
                                  Title: Vice President

                              TL VENTURES III INTERFUND L.P.

                              By:  TL Ventures III L.L.C.,
                                   its general partner

                              By: /s/ Christopher Moller Ph.D.
                                 ------------------------------------
                                  Name:  Christopher Moller Ph.D.
                                  Title: Managing Director

                              SCHEER INVESTMENT HOLDINGS II, L.L.C.

                              By: /s/ David I. Scheer
                                 ------------------------------------
                                  David I. Scheer
                                  Managing Member

                              /s/ Cesare Sirtori
                              ---------------------------------------
                              Cesare Sirtori, M.D.



     [Signature page to Amendment No. 1 to the Investors' Rights Agreement]
<PAGE>

                                                                       EXHIBIT A
                                                                       ---------
                             SCHEDULE OF PURCHASERS

<TABLE>
<CAPTION>
------------------------------------------------------------------------------------------
                                                 No. of                     Cash
Purchaser's Name and Address                 Series B Shares           Consideration
----------------------------                 ---------------           -------------
------------------------------------------------------------------------------------------
<S>                                      <C>                      <C>
Oak Investment Partners VII, Limited                   3,685,125            $5,487,187.503
Partnership
c/o Oak Investment Partners
One Gorham Island
Westport, CT  06880
Attention:  General Partner
------------------------------------------------------------------------------------------
Oak VII Affiliates Fund, Limited                          91,875            $   137,812.50
Partnership
c/o Oak Investment Partners
One Gorham Island
Westport, CT  06880
Attention:  General Partner
------------------------------------------------------------------------------------------
TL Ventures III L.P.                                   3,019,385            $ 4,529,077.50
c/o TL Ventures LLC
800 The Safeguard Building
435 Devon Park Drive
Wayne, PA  19087-1945
Attention:  Chief Financial Officer
------------------------------------------------------------------------------------------
TL Ventures III Offshore L.P.                            632,026            $   948,039.00
c/o Trident Trust Company (Cayman)
Limited
P.O. Box 847
One Capital Place, Fourth Floor
Grand Cayman, Cayman Islands
------------------------------------------------------------------------------------------
With a copy to:

TL Ventures LLC
800 The Safeguard Building
435 Devon Park Drive
Wayne, PA  19087-1945
Attention:  Chief Financial Officer
------------------------------------------------------------------------------------------
</TABLE>
<PAGE>

<TABLE>
<CAPTION>
------------------------------------------------------------------------------------------
                                                 No. of                     Cash
Purchaser's Name and Address                 Series B Shares           Consideration
----------------------------                 ---------------           -------------
------------------------------------------------------------------------------------------
<S>                                      <C>                      <C>
TL Ventures III Interfund L.P.                            98,589            $   147,883.50
c/o TL Ventures LLC
800 The Safeguard Building
435 Devon Park Drive
Wayne, PA  19087
Attention:  Chief Financial Officer
------------------------------------------------------------------------------------------
HealthCap KB                                             896,000            $ 1,344,000.00
Sturegatan 34
S-114 Stockholm
Sweden
------------------------------------------------------------------------------------------
HealthCap CoInvest KB                                  1,237,333            $ 1,855,999.50
Sturegatan 34
S-114 Stockholm
Sweden
------------------------------------------------------------------------------------------
Cesare Sirtori, M.D.                                     333,333            $   499,999.50
[Address]
------------------------------------------------------------------------------------------
Scheer Investment Holdings II, L.L.C.                     33,334            $    50,001.00
Cc/o Scheer & Company, Inc.
250 West Main Street
Branford, CT  06405
------------------------------------------------------------------------------------------
TOTAL                                                 ----------            --------------
-----                                                 10,000,000            $15,000,000.00
                                                      ==========            ==============
------------------------------------------------------------------------------------------
</TABLE>