William L. Wright has been appointed director of government affairs in the Washington office of Eli Lilly and Co.

David R. Waters, chairman and chief executive officer of Garfinckel, Brooks Brothers, Miller & Rhoades Inc., has been elected to the board of directors of the Firestone Tire & Rubber Co.

Hugh H. Smith has been named senior vice president for government affairs of American Express Co.

Bette B. Anderson, former undersecretary of the Treasury and currently a management consultant in Washington, has been elected to the board of directors of International Telephone and Telegraph Corp.

Irving S. Shapiro will become a partner in the New York law firm of Skadden, Arps, Slate, Meagler and Flom when he steps down as chairman and chief executive officer of the Du Pont Co. on April 30. Shapiro will stay on as a member of Du Pont's board of directors as well as the boards of Citicorp and Citibank, International Business Machines Corp. and Continental American Life Insurance Co. He will continue to serve as a trustee of the Ford Foundation and the University of Pennsylvania.

William H. Hanley has been named vice president for government relations for Gould Inc., a developer and manufacturer of electrical and electronic products. He will work out of the firm's government relations office at 2550 M St. NW.