Just use Crisco for patch lube and bore preservative. It is shortening, after all.
Sorry, I couldn't help myself...Ok, so I could, but didn't.
I just trued up the muzzle of an old Douglas barrel using the file and square. The crown/slight cone was applied using a cone shaped grinding stone for a dremmel tool. The stone was held stationary, by hand, and the barrel rotated, by hand, with the unbreeched breech end of the barrel placed on a piece of board, to get a concentric crown/taper.
Using your lathe, a tool similar to a counter bore can be made to square the muzzle. If the cutting end of the counter bore is large enough, it can be used, with removable pilots, to square the muzzle of nearly any diameter barrel.
There is a tutorial on making a crown tool in the tutorial section, but I prefer to do it the quick and easy way.
God bless