Good ol' Hoppes No. 9 to clean the barrel. Haven't had to do it yet on the 15-22, but I'll used Hoppes Copper Solvent for copper fouling.
Then I'll use Outers gun oil or CLP to lightly lubricate the barrel. I'll use a lighter oil, like RemOil, on a clean rag to wipe a light coat on the bolt & charging handle. I'll then use the rag to wipe out the upper receiver.
IMO, the lower really doesn't need much cleaning. When it does, I disassemble the fire control parts, wipe the parts clean, & wipe out the lower. Prior to reinstalling the fire control parts, I'll then put some RemOil on a rag and wipe them down.