LeQuire was born in Nashville and obtained an M.A. in art education from George Peabody College at Vanderbilt University. In addition to being a well-known portrait and landscape artist, LeQuire taught studio art and art history at Montgomery Bell Academy from 1967 to 1979 and worked as an artist and teacher at the Nashville Institute of the Arts from 1980 to 1992. Following that position, she became the arts editor at Nashville Life magazine. Her independent article on sculptor William Edmondson was published in Smithsonian magazine in 1985. Her paintings can be found in the collections of Vanderbilt University, Montgomery Bell Academy, and the Tennessee State Museum.
In 1997, LeQuire produced a documentary film on Red Grooms, which was nominated for an Academy Award. The Louise LeQuire Award for Achievement in Screenwriting was established in 2010 to be awarded annually at the Nashville Film Festival.