I really got into fire lapping a decade or so ago. I used the Tubb system and the NECO system, and came to prefer the NECO, as it allows "customizing" for various needs.
Two claims are commonly made for fire lapping. The first is that it smooths the barrel and decreases fouling. This is mostly, usually, depending on what you do and what you do it to, true. A bad fouler often responds to lapping, but sometimes doesn't. and sometimes it takes so much fire lapping that you end up moving the throat forward by a significant amount, which causes its own problems.
The second claim is that it increases accuracy, by creating a taper from breach to muzzle. This sounds plausible, but I could never prove it. Again, by the time you have removed that much metal from the bore, you can expect to have moved the throat forward by a bunch, which tends to negate any potential accuracy benefits from a tapered bore.
So I've pretty much given up on fire lapping. If the bore is so rough that it fouls badly, fire lapping may or may not solve it, and it's enough work that I tend not to see it as a worthwhile gamble. So these days, bad barrels get replaced or traded off. And if I'm looking for top accuracy, I start with a hand-lapped barrel anyway.