I looked at the 1920 census for Clemons. He stated that his father was b in France and spoke French. So that got me thinking. I believe that the last name was really Le Mans (pronounced Ley-mons) and got Americanized to Lemons.
I would try checking with the Aiken County Courthouse and the Richmond County Courthouse for a marriage license for Moses and Louise Kicklighter, between 1933-1940. The marriage license may very well tell you who the parents are.