A few things ya got know before you shoot lead bullets in your gun. First what is the diameter of the bullet? And what's the groove diameter of the barrel. and what is the diameter of the cylinder throats? Fit is king when it comes to lead bullets. If your bullets are too small, they will lead the barrel. If your bullets are too small, no matter how hard/soft, what velocity you shoot them, regardless of how good your lube is, it's gonna lead the barrel. I would suggest you slug the barrel, and measure the cylinder throats. For a very good start, size or purchase bullets the same size as the cylinder throats (nearly every modern production gun's cylinder throats will be larger in diameter than the barrel's groove diameter, insuring a good bullet/bore seal and eliminate leading).
I have shot a whole bunch of .44 Magnum and 357 Mag./38 Special cast lead bullets, mostly air cooled range lead w/wheel weight alloy, 9-12 BHN (4 of my .44 magnums and 2 .38 Specials have not fired a jacketed bullet in about 18 years, and two never fired a jacketed bullet while in my possession.). When they fit the gun, they don't lead. I even shot an OOPS! load in my .357 Magnum ( a slightly over max. load of True Blue under a 150 gr. cast SWC, wheel weight alloy, air cooled, plain base, with C-Red lube), at a guesstimate of over 1200 fps, and closer to 1300, and the barrel was clean after 12 shots. The bullets were sized to the cylinder throats, .3585", with a groove diameter of .357"....
There are other factors (like bullet skidding) but if you start with fitting the bullet to the gun, you'll have a very good chance of eliminating leading and won't have to look any farther for a "clean shooter"...