I think JB Bore Bright, available from Brownell's, may be more suitable for barrel lapping. It is a much finer abrasive and gives a very smooth finish. A little goes a long way. I usually start by thououghly cleaning the barrel, then running a tight patch with the Bore Bright through about 6 times. Nice full, even strokes. I did that on my Ruger MK III512 and it changed it to a tack driver.
I haven't seen the need to lap my Green Mountain barrel.
