An avid outdoorsman and an amateur pilot, Burch traveled widely to engage in hunting, fishing, hiking, camping, and scuba-diving. As a young man, he worked in Alaska for the U.S. Biological Survey and the Territory of Alaska, shooting bald eagles, which were considered a nuisance. In later years, he was to become a strong supporter of wildlife conservation. Late in his life, Burch was a leader of efforts to save the Shelby Farms area of Shelby County from development, a conservation initiative that culminated in the establishment of the Shelby Farms Park on . The Lucius E. Burch State Natural Area, a state natural area within Shelby Farms Park, is now named in his honor. Among the awards that he received were the Carter Patten Award of the Tennessee Conservation League, the "Lawyer's Lawyer" Award of the Memphis and Shelby County Bar Association, the Certificate of Merit of the Memphis Urban League, an honorary doctorate from Rhodes College, and honorary life membership in the Tennessee Academy of Sciences. Burch married Elsie Caldwell in 1935. The couple were the parents of four daughters. They resided in Collierville, Tennessee, and also maintained a summer cottage at Beersheba Springs that had belonged to Lucius' parents. His daughter, the late Lucia Burch, was the longtime lover, muse and collaborator of the photographer William Eggleston. In the late 1990s, after her husband's death, Elsie Caldwell Burch donated $575,000 toward the construction of a new public library in Collierville. The library, completed in 2000, is named the Lucius E. Burch Jr. and Mrs. Elsie C. Burch Library in honor of the Burch donation.