You can buy lapping compound in finer grits than the standard 240 grit popular in automotive machine shops. I use 2-3 different grits, depending on what I'm trying to accomplish, usually 320, then 400, followed by 600. Lap in stages, don't try to do everything at one sitting or you'll err to one side of the other. Needing more lapping is good, lapping too much is obviously bad.
My first lapping generally runs with six coarse, 12 medium, and 12 fine grit. I swap the bore with Eds Red between shots, followed by a dry patch. Since you can't control the amount of residual compound in the bores, I make sure every lapping shot is in a clean bore. And any leading you may encounter from lapping bullets must be removed before the next shot. To be honest, I roll my lapping bullets between steel plates for full coverage, so I haven't experienced any leading from lapping bullets, but have heard enough testimonials from others who have. The cylinder chamber & throat need cleaning too, since the will "lap" as well, just at a rate of 1 to 6 with the bore. I number my chambers with a marker to make certain each cylinder gets the exact same lapping bullet count.
After you run your course for the session, clean and slug the barrel again to check your progress. It is important to know your starting point so you can evaluate your progress. You may want to up the count on coarse compound bullets for the second trip. With stainless, it's almost guaranteed. With Ruger stainless (Terhune Anticorro, a proprietary alloy), you will definitely want to double or even triple the number of coarse compound bullets on the second trip, it's really abrasion resistant!
Eventually you will see the polishing action taking place from the forcing cone forward, don't try to polish the entire length of the bore, you'll likely end up with an oversized bore at the entry. Just lap enough to achieve your immediate goal. The bore will be tapered minutely from forcing cone to muzzle, that's what we're really after. My Super Redhawk took a ton of lapping, and when It was done less than half of the bore showed any change at all. I hated to leave it like that, but it was all that was needed to make it perform, and I had recently replaced a Ruger P90 barrel for a guy who had overdone his lapping, wanting the barrel to be polished smooth & shiney full length. A .454 round ball literally rattled in the bore.