In theory, soft lead bullets swage up to the cylinder mouth diameter before entering the barrel. If there is a mismatch between cylinder chamber mouth diameter and barrel groove diameter, the soft lead bullet is more likely to swage to a proper fit.
Hard lead bullets, on the other hand, don't swage up to fill the chamber mouth, and are unable to swage to barrel groove diameter for a proper fit.
Soft lubes (traditional 50/50 alox/beeswax) are more effective than the crayon-like lubes favored by commercial bullet makers. The harder lubes simplify volume loading of ammunition and trade off lubrication efficiency.
I've found this to be true, that soft lead bullets with soft lube generally gives superior accuracy in most guns.
HTH
John