Okay, well, I've always lapped my lugs with the barrels off and actions stripped, I'm not sure if its advisable to try it with the barrel on or not, primarily because you have to clean that lapping compound out of the action. Someone else may have done it with the barrel on?
I use Brownells lapping compound, I have both 600 and 800 grit.
What I do is with my stripped action, AND a stripped bolt (remove the remington plunger and firing pin). I dabb a little bit of 600 grit and the lugs on the inside of the action. I then put in my lapping tool, then the bolt. I push the bolt ALL the way in before closing it the first time. I then let the lapping tool push the bolt back against the lugs. I then just open and close the bolt 50 times and then pull the tool off and the bolt out. Clean, and then check wear. If I have made good progress (you can see the wear pattern on the bolt lugs) then I will switch to 800 grit and do the same thing. I will use 800 grit until I get at least 80% coverage. Then clean a final time and call it good
The first problem would be as mel said cleaning the lapping compound out ,second and a big one is the possibilty of increasing headspace, if done with the bolt in a barreled action and thats not good even dangerous
if carried to far.