Robert L. Randall, 54, an Environmental Protection Agency lawyer, died Wednesday on his yacht, the Sea Call, in Fort Lauderdale, Fla., as the result of a self-inflicted gunshot wound, according to the Broward County medical examiner.

Mr. Randall, who was on vacation at the time of his death, was an expert on aircraft noise control and was chief of the airport and consumer affairs branch of the EPA office of noise abatement and control.

A native of Rochester, Minn, where his father was a doctor and board chairman of the Mayo Clinic, Mr. Randall served in the Army Signal Corps in the South Pacific during World War II. He later earned undergraduate and law degress at the University of Chicago.

Mr. Randall as an editor of the Chicago Law Review and taught law for two years at the University of Indiana. He came to Washington in 1953, and joined the staff of the Securities and Exchance Commission. He was a law clerk to Associate Supreme Court justice Stanley Reed for the 1953-1954 term.

Later, Mr. Randall joined the Washington law firm of Covington and Burling, where he worked until he became deputy general counsel of the Federal Aviation Administration and a member of the White House jet aircraft noise panel from 1963 through 1967.

Mr. Randall later was a partner in the law firm of Surrey, Karasik and Morse until 1973, when he joined the EPA.

He was a former member of the board of the Washington Opera Society.

Mr. Randall is survived by his wife, Mary H., of the home in Washington; two daughters, Priscilla and Louisa, of Washington; a son, Robert of Washington; his mother, Faith Meek Randall, of Rochester; a sister, Mrs. F.D. Fulton, of Sacramento, Calif., and a brother, David, of Minneapolis.

The family suggests that expressions of sympathy be in the form of donations to the Sheridan School Scholarship Fund or to the Woodrow Wilson High School Home and School Association.