I am researching a Gilmer/Gilmore family and came across your message.I have some information on a G.W. Gilmore family that I have collected trying to rule them out or in.I'm not sure if this is the family that you are looking for, but thought I'd pass along the info just in case it might help you.
1850 Wilcox Alabama Census, Unknown Township, page 987 (I was not able to access records) G.W. Gilmore
1860 Calhoun Alabama Census, page 492, Twnship 13, Range 11 G.W. Gilmore, 35, SC Margaret, 25, MA Elizabeth, 11, SC William, 10, SC Mary J., 8, SC Lemuel, 6, SC Jasper, 2, AL
1870 Cleburne Alabama Census, page 350, Twnship 13, Range 11 Margaret Gilmore, 36, AL Elizabeth, 22, AL William, 20, SC Mary, 17, SC Lemuel, 15, SC Jasper, 11, AL George, 10, AL Josephine, 8, AL
In your query you mentioned the name Lemuel Buckhanon.Notice this G.W. Gilmore/Gilmer had a son named Lemuel.