Nothing wrong with painting the inside if you really want to. I don't, just my personal preference. My chickens don't seem to care but some people do. It's your option, not a requirement.
If it's been vacant for a while it probably doesn't need disinfecting, but I'd still consider that a good practice. If I were doing it I'd use a bleach-water solution and soak it pretty good, then let it dry on it's own. It takes a little while for bleach, lysol, or oxide to work so do not rinse it off immediately. If you rinse at all give it a few minutes to work.
I don't know what that coop looks like, how big it is or how it's built. Be careful to not get the spray on your skin, in your eyes, and don't breathe it. If you do paint it inside be careful breathing the fumes. And in any case let it really air out before you put chickens in there. Chickens have a more delicate respiratory system than you do, fumes are more dangerous to them.