The reason squib loads are mandatory for lapping with cast bullets is to prevent severe bore leading. ( Lap compound is the opposite of a lubricant.)
Those who sell or reccomend jacketed bullets for lapping run them at high speed and I suppose velocity isn't a big concern with jacketed as leading isn't a problem, and high pressure might obturate the bullet out into the grooves to get a bit of lapping in this critical area.
But I firmly reccomend, even warn against using jacketed to lap barrels. For several reasons:
The hard jacket material will cause severe cutting at the rifling origin as the jacket is being swaged down, causeing excessive roughness, and excessive throat wear. The jacket will swell after passing through a tight spot and continue lapping where we want no cutting action. The jacket will not lap tightly into the corners of the rifling, which is the most crucial area for cast bullets, in that any roughness will rip off lead from the bullet, or cause stripping. Lead bullet hardness of over about 12 bhn will also expand after passing through a tight spot, creating a lumpy barrel, dimensionally, though hard bullets do lap very aggressively..
I have found that 12 bhn is the maximum hardness which will swage down and stay down when going through tight spots. This means only the tight spots will be lapped at first. After they are opened up, the entire barrel will get it's attention, and the result is a very slight taper bore, tight at the muzzle, with throat and rifling origin smoothed and a bit more tapered than the length of the barrel.
Even the highest quality custom barrels will be improved by lapping with the LBT bore lap kit, and the poorest will become stunningly improved, often to near match quallity. This is speaking of any rifled bore, in handgun or rifle.