I knew it had to be something that replaced the locker NIF. I could think of no other explanation...
Since most people use the 'unofficial patch', what could I do to resolve this issue of the texture sets not showing on the locker?
There must be some reason why they changed it in the patch...
From the Unofficial Patch Readme...
Fallout 3: Fixed missing underside and interior of the vault locker (Altered Mesh: lockervault01.nif).
This actually causes a bit of a problem, but it can be fixed with a little bit of rework.
The original lockervault01.nif had these 2 slots for new textures,
LockerVault01:0
LockerVaultDoor:0
Your labeled texture is assigned to LockerVaultDoor:0
The new mesh has these slots,
LockerVaultDoor:0
LockerVault01:05
LockerVault01:04
LockerVault01:03
LockerVault01:02
LockerVault01:01
LockerVault01:0
Your original LockerVaultDoor:0 assignment now becomes LockerVault01:0 on the new mesh.
There is really only one fix for this. You need to use the new mesh yourself, change your labeled texture from LockerVault01:0 over to LockerVaultDoor:0. You would then include the new mesh along with your vault. If the user already has the Unofficial Patch installed it will just overwrite the mesh they already have. If they don't have or don't want to run the Unofficial Patch, they will at least have just the one mesh needed for your vault lockers.
EDIT: There is another option. You could use FO3Edit to make a compatibility patch with just the lockers in it and change the texture assignment in just the patch. FO3Edit would also be a fast way to change the texture assignment. In the Alternate Textures section for each locker, change the 3D Index from 0 to 6.