As far as lead lapping I was able to see it done by a master. His big thing was sporterizing Mausers, Springfields and started getting into match rifles. The one thing that I see that is not done in shops 40+ years later is that he would always lap a barrel vertical. His reasoning was that the lapping compound would go to the bottom of the bore/lap if done while the barrel was horizontal and as a result would be uneven.

The thing that gets you with a lead lap is the change of direction. As you go thru one way and then go to pull it back the grit "shifts" exposing new cutting edges and as a result cuts more till the grit imbeds itself in the lap. That is why they cut one end and chamber the other when they lap a blank.

Now fire lapping is a bit better in that you only go one direction. The grit will be fresh starting out so it will remove more metal at the chamber end. That can be to your advantage as long as you do not destroy the throat. If you end up with being a few .0001" tighter at the muzzle that is the berries IMO.