One thing that supposedly makes the firelapping work is that it will produce a tapered bore and can smooth a rough scaly throat. Bore gets more snug as the bullet approaches the muzzle. Supposedly, this type of tapering is one of the tricks that the P14 and 1917 Rifles had as well with their original barrels.
Personally, after doing the research, I would only use it if I had accuracy problems in the first place, a rough bore and throat, and for some reason could not replace nor rechamber the existing barrel. I would not want to do so with a new precision barrel.
I was about to do it to an old 11/1918 Eddystone barrel but instead bought a better WWII era High Standard barrel which were not tapered to fit my 1917 rifle. This made the whole firelapping project a nonstarter--kept the barrel if I ever want to restore the 1917 to WWI configuration. Since the receiver was parkerized anyway, I decided to go with the WWII look in my restoration.