Booth shows:
Hairington, Luke. Pvt. Corpl. Co. G, 27th La. Inf. En. Jan. 1, 1863, Monroe, La. Present on Roll to Feb., 1863. Appears on Roll for July and Aug., 1863.
No listings under the other spellings.
Co. G was from Keatchie in DeSoto Parish and was formed in March 1862 and moved to Vicksburg on May 1, 1862 where they remained until the end of the siege.
It looks like he joined the army, probably to avoid conscription, and was assigned to Co. G of the 27th. NCOs were generally elected by the men of the company and he attained the rank of Corporal.
I don’t remember anything in my book about him specifically, but I followed the Dixie Rebels as closely as I could and there is a lot of material about them in the book. You will get a very good idea of what your GGG grandfather experienced from reading the other soldier’s accounts in the book.
Hope this helps and let me know if I can assist you in the future.