Both his and his wife's Pension applications list his regiment as Company A, Lawrence Missouri Cavalry. I would believe the "Lawrence" tag to be in error.

Arkansas, Confederate Pension Records, 1891-1935

Name: William M . Foley
Spouse Name: America Foley
Residence Location: Lawrence , Arkansas
State Served From: Missouri
Division: Cavalry
Company: A
Regiment: Lawrence
Death Date: 5 Mar 1928
Spouse Death Date: 1931
Comments: widow applied 1928