You'll notice that we also have push through slugs for all calibers, which are companion to the lap kit. and I reccomend that anyone considering lapping a barrel feel out the bore first with a push through slug.
I have never encountered a barrel that didn't benefit from lapping with the LBT lap kit and method, which uses relitively soft lead bullets only. I definately reccomend against lapping with jacketed bullets, because they rip the throat of the gun out yet don't touch the most critical area, which is the leading edges of the rifling, corners and bottom of the grooves.
One customer lapped three very expensive 22 RF target rifles and cut groups in half or less, and all shot at or under a half inch at 100 yards before lapping!
So, yes, I definately would lap the premium Shaw barrel. If it were perfect, which none are, chambering, crowning, and any other machining work on the exterior of the barrel will change the inside. Lapping the finished gun fixes all these harmful changes while touching up tiny irregularities inside the gun.
This almost eliminates breakin, but follow the lap kit instructions on that matter, using Tetra lube in place of the reccomended S&W Friction block, which has been discontinued. Tetra is it's equal.