First a simple but important principal: One lap - one grit. NEVER use a lap for different grits as the grit embeds into the surface of the lap.
Copper laps are used for pre-polishiing, 3000 or 8000 normally, then you move to the polishing lap of which there is a plethora, covering both synthetics and metal alloys.
I have one synthetic, a Lightning Lap precoated with Cerium, all other polishing laps are either Tin, Zinc or cast iron depending on the stone and I use 50k DeBeers diamond in the most minimal amount, ie, a little bit of baby oil on the lap, smear with diamond then wipe off, the fractional amount that remains embeds into the surface and polishes fast provided the pre-polish and polish laps are flat and true.