There is no one in the regiment named Luke and only one Hitchcock

William L. Hitchcock/Hitchcloth, Private, Captain D. M. Southard’s Company, 25th Regiment Tennessee Infantry,* joined for duty and enrolled November 8, 1861 at Mill Springs, Ky. by Col. Stanton, enlisted in regiment December 30, 1861, discharged August 18, 1862 by reason of being non-conscript, no further records

* This company was also known as Company E, 25th Regiment Tennessee Infantry.
The 25th Regiment Tennessee Infantry was organized for State service August 10, 1861, transferred to the service of the Confederate States October 1, 1861, and re-organized May 10, 1862.

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Tennessee

……..

I suspect this may be him:

1860 United States Federal Census

Name: William Hitchtock
[William Hitchcock]
Age: 15
Birth Year: abt 1845
Gender: Male
Birth Place: Tennessee
Home in 1860: District 7, White, Tennessee
Post Office: New Ark
Family Number: 989

Household Members:
Name Age
Zuccariah Hitchtock 67
Martha Hitchtock 38
Catherine Hitchtock 18
William Hitchtock 15
James R Hitchtock 14
Rebecca Hitchtock 11
Samuel H Hitchtock 9
Jessie S Hitchtock 8
Lewis I Hitchtock 6
Andrew I D Hitchtock 4
Rutha Hitchtock