William Sterling Byrd Lacy, 68, who negotiated a major cultural agreement with the Soviet Union and who was a former ambassador to Korea, died of cardiac arrest Monday at his Washington home.

The 1958 cultural exchange pact with the Soviet Union called for an exchange of scientists, students, sportsmen, artists, tourists, and publications. It also permitted the United States to take to the Soviet Union a number of exhibitions on American life, in the first of which then vice president Richard M. Nixon held his famous "kitchen debate" with Soviet Premier Nikita S. Khrushchev, on July 24, 1959.

The cultural exchange agreement was reached in the midst of the Cold War and Mr. Lacy received much of the credit for it. Lyndon B. Johnson, then the Senate majority leader, called it a "positive step" in breaking down "barriers of suspicion and distrust in a war-weary world."

Mr. Lacy carried out the negotiations as special assistant for East-West Exchanges to Secretary of State John Foster Dulles. His appointment was in line with a National Security Council recommendation and a suggestion from the Big Three foreign ministers.

His service abroad included tours of duty in Indonesia and the Philippines. While serving with an American mission in Indonesia after World War II, he advocated that the United States support an independent state support an independent state rather than the restoration of Dutch colonial rule.

In the Philippines, where he served as counselor of embassy, Mr. Lacy favored U.S. support for the liberal Ramon Magsaysay in the 1953 presidential election.

Mr. Lacy was named ambassador to Korea in March 1955. He came into conflict with the Korean government almost at once over American businessmen's disputes with the Korean government. Because of this and other difficulties, including an inability to work with Korean President Syngman Rhee, he requested that he be recalled. He suggested to the State Department that a "diplomatic illness" be used as an excuse for his replacement. The department agreed.

He resigned as ambassador in November 1955, and returned to Washington to work as special assistant to Dulles.

In addition, Mr. Lacy was a member of the board of examiners of the Foreign Service and was deputy commandant of the National War College before retiring in 1961.

A member of an old Virginia family, Mr. Lacy was born in Mesa County, Colo. His father had gone West, made a fortune in insurance, and had become lieutenant governor of the state. Mr. Lacy spent part of his boyhood at the family homes, Elwood, near Leesburg, Va., and Chatham, which is across the Rappahannock River from Fredericksburg. He was a graduate of the University of Colorado.

An economist by training, he began his career in Washington with the late Sen. Alvah B. Adams of Colorado. Mr. Lacy later worked on economic problems for a number of agencies, including the War Production Board.

He joined the State Department in 1946, having caught the eye of Secretary of State George C. Marshall while serving as assistant deputy director of the United Nations Relief and Rehabilitation Administration.

Despite his western beginnings, Mr. Lacy had the manners and accent of a Tidewater Virginia gentleman. His red hair and mustaches once prompted a State Department colleague to remark that he looked like "a cashiered guardsman" or a "river-boat gambler." He had a reputation for hospitality, a seemingly endless supply of southern stories, and ability.

He was a member of Christ Church in Washington, the American Academy of Political Science, and the Metropolitan Club.

His marriages to Margaret Innes Lacy and Kirsten Magelssen Lacy ended in divorce.

He is survived by his wife, Elizabeth L., of the ho,e; a son, Sterling Byrd Lacy, of Sussex, England, and a daughter, Kirsten Bagley, of Huntington, W. Va. CAPTION: Picture, WILLIAM S.B. LACY 1964 Photo