I found three L. Yates in Mississippi Confederate Units.

George Martin

L Yates

Residence was not listed;
Enlisted as a Private (date unknown).
"C" Co. MS 16th Infantry

L D. Yates

Residence was not listed;
Enlisted as a 2nd Lieutenant (date unknown).
"D" Co. MS 1st State Troops Infantry

Lawrence T. Yates

Residence was not listed;
Enlisted as a Private (date unknown).\
"G" Co. MS 1st Cavalry