Lila Hinze Youngquist, 58, executive director of the Montgomery County Medical Society and a longtime officer of the county League of Women Voters, died Tuesday at her Kensington home. She had cancer.

Mrs. Youngquist began her career in medical administration in 1966 as coordinator of the medical society's medical care coordinating office. She then directed the medical care coordinating agency of the Mutual of Omaha insurance company's Washington office, and later Montgomery County's health fund. In 1971, she rejoined the Montgomery County Medical Society as its executive director.

She was born in Pine City, Minn., and earned a bachelor's degree in institution managment from the University of Minnesota.

Mrs. Youngquist served in the WAVES DURING WORLD WAR II and was assigned to the Navy's office of public affairs here.

Before returning to this area in 1958, she held a number of volunteer offices with the League of Women Voters in Morristown, N.J. She later served as finance chairman, public relations chairman and board member of the Montgomery County chapter of the League of Women Voters.

Mrs. Youngquist also served on the board of the Montgomery County Community Arts Association and on the Montgomery County PTA Association's executive committee. She was a member of the Association of Medical Executives, the Potomac Appalachian Trail Club and the American Beekeepers Association.

Survivors include her husband, Robertson Youngquist, of the home in Kensington; two daughters, Margaret and Elizabeth, also of Kensingson, and two sisters, Paula Brandt, of Willmar, Minn., and Susan Dooley, of Eau Claire, Wis.

The family suggests that expressions of sympathy be in the form of contributions in Mrs. Youngquist's name to The Nature Conservancy, Arlington. CAPTION: Picture, LILA H. YOUNGQUIST