Someone may have responded to your query already but I'll write anyway.I have Langleys in my husband's line but they were not in Georgia and Arkansas (that I know of!)
Luther's father was Enoch Langley.In the 1880 AR>White>Cadron Census you will find one-month-old Luther C. living with his parents, E. Langley and wife A.T.J.A further check of the later censuses tell us that E. is Enoch Langley.
If you will Google:White County AR Genealogy Project, Biographical & Historical Memoirs of Eastern AR
I also found (Google) several sites for cemeteries (Mt. Hebron at Joy, AR; Oak Grove, Searcy where Luther & wife are buried; and Sidon at Sidon,AR) where a lot of your Langleys are buried.I feel sure you have discovered these cemeteries already.
On Ancestry.com I found two World War Draft Registrations for Luther if you don'thave them already. 1917 & 1942
I don't know who Enoch's father was.IF I find out anything I'll write again.