So you played on an old ass Mesa that was never geared for high gain and you are assuming they are all like that?
From your earlier description it sounds like the Rhythm channels aren't necessarily bad.
If it is Mark iii, it should have five 12ax7 triodes. Try swapping V3 (Lead channel) with V4 (reverb driver). Maybe that will help the Lead channel.
Did you have an od hooked up. Really turns into a different kinda monster.