Munds was born Frances Lillian Willard in Franklin, California, on June 10, 1866, the eighth child of Joel and Mary Grace Vinyard Willard and a granddaughter of Alexander Hamilton Willard (1777–1865) who had been a member of the Lewis and Clark Expedition. Her family were ranchers who moved to Nevada before moving on to the Arizona Territory. Willard was educated at the Central Institute in Pittsfield, Maine, graduating in 1885.