Clean - Oil on a rag
Store - Birchwood Casey's 'Barricade' (recall it used to be called 'Sheath') on patches or RIG for long-term storage
Lead Removal - I do like those 'Lead Wipe Away' yellow patches with some lead remover product (??) on them, for handgun bores IF they lead ...
Muzzleloader Barrels (where pinned into the stock) - As a MZL build, this is what I do or do to any new-to-me acquisition. I remove the barrels carefully, noting that ALL BARREL PINS - antiques to modern - are removed from Left to Right as you look down the barrel towards the muzzle. Re-insert them or install them (new builds) from Right to Left. Anyways, I'll then clean the barrel well, then wax it, then apply Barricade (a liquid wax protectant) and then for extra insurance, I'll RIG the under-side of the barrel where it sits in the stock. A caveat for this is that the barrel channel must be finished.