I've lapped many ML barrels. I used to buy low quality barrels and lap them. Real lapping is done by casting a lead slug on a rod. I use alloyed lead. I use all thread with nuts, washers and a leather washer between to prevent leakage when casting. The old string method does not center the lap well. Use a good steel rod with a guide and work from the breech end. I make the guide to screw int he plug threads. I do use coarse valve grinding compound to start, maybe #120 silicone carbide. I am trying to remove significant material. Tight and loose places are very prominent in button barrels. I use a tapered screw to tighten the lap. I work the bore really aggressively. I figure on raising a blister on my hand. I am trying to put a small choke, maybe 0.001" that my short starter can get past. That takes a long time an a lot of sweat to do that. Once it feels even and choked the way I want I go on to about #320 grit. That will be pretty smooth and shiny. I have tried very fine abrasives an only produce sweat and blisters with little return for my effort.
A smooth, uniform, choked barrel is a pleasure to load and shoot.
You can certainly steel wool, Flitz, or scotch brite a barrel, it is not lapping though. I would not lap a good barrel as I described above. A pitted nasty old barrel can be saved this way.
