Lila May Banks Cockrell (January 19, 1922 – August 29, 2019) was an American politician. She was Mayor of San Antonio, Texas from 1975 to 1981 and again from 1989 to 1991. During World War II, she was in the WAVES branch of the United States Navy. She was President of the Dallas and San Antonio chapters of the League of Women Voters during the 1950s. She was born in Fort Worth, Texas.