A. Lothrop Luttrell plans to retire as chairman of the board of Woodward & Lothrop Inc., at the May 22 annual meeting of the department store company.

An employe of Woodies since 1938 and a director since 1942, Luttrell also is one of the company's largest stockholders. He will be within 10 months of normal retirement age for company officers at the annual meeting.

Luttrell will be succeeded as Woodies' chairman by Edwin K. Hoffman, who will continue as chief executive officer. Hoffman joined the firm in 1968 and became president and chief executive the following year.

The Woodies' board will promote Waldo H. Burnside to succeed Hoffman as president of the retail firm at the annual directors' meeting, according to a company announcement yesterday.

Burnside has been executive vice president since 1974 and a director since 1969. He started with Woodies as a management trainee in 1949 and has been a buyer and division vice president.

Luttrell is a grandson of Alvin Mason Lothrop, one of the founders of Woodies. He has been chairman since 1965, Luttrell will remain on the board and on the executive committee.

In another top management change, Edgar F. Peterson has been elected president and chief administrative officer of National Permanent Federal Savings and Loan Association, the area's second largest thrift institution.

He succeeds John W. Stadtler, who will continue as chairman and chief eexecutive of the $646 million S&L. Peterson joined National Permanent in 1955 as controller and was elected vice president in 1960, a director in 1969 and executive vice president in 1970. Peterson, former president of the Metropolitan Washington Savings and Loan League, will be in charge of daily operations, while Stadtler concentrates on corporate policy and planning.