Quick correction, I don't think they can be demoted beyond that of a 2nd Lieutentant (O1), so even an enlisted rank like Private wouldn't be possible. If you want to keep him as a Lieutenant later in the story you would need to keep him as a Lieutenant at the beginning. Maybe just bust him from 1st Lieutenant (O2) to 2nd Lieutenant (O1). But most people aren't going to see the difference as he is just referred to as Lieutenant.
If you want the demotion to be more consequential you could make him a Captain (O3) who then got busted to Lieutenant (O1) - from the reading I've been doing this type of demotion is often accompanied by prison time. It doesn't happen very often, and would be significant if it happened, and tie in pretty well with whatever it is that put the MC in Leavenworth to begin with. So Kira would need to refer to him as Captain later, and the guards/major at the beginning would call him Lieutenant, although I'm not sure if you are referred to by rank in Leavenworth or not, might just be by name.
Keep in mind that Lieutenants, in general, lead platoon sized elements (officially 20-50), whereas a Captain leads a company/troop sized element (multiple platoons). Unless they are special operations, I think the lines blur there a bit more. So you would need to keep that in mind for storytelling purposes moving forward.
Alternatively you could keep him as Sergeant or Private in the early game and change the rank he was busted from to Sergeant First Class (E7 - still referred to as Sergeant though - highest ranked NCO in a platoon, leads alongside a Lieutenant) or go a bit higher to First Sergeant (E8 - actually referred to as First Sergeant - highest ranked NCO in a company/troop, leads alongside a Captain). A demotion from E7 or E8 to E1 would be super dramatic, a bit unrealistic, but would emphasize that whatever shit he stepped in was really sticky.
