There have been some pretty good notes on lapping in the past, so a search of the archives will likely turn up some good information.
You may get other ideas on this, but here is what I'd do:
First, do you also need to lap the cylinder bore? There is little point to lapping the piston if the bore is rough.
To lap the bore, get yourself an expanding barrel lap of the correct size. Places like www.mscdirect.com sell them. You could make one, but they're cheap enough so it's hardly worth the effort. Set up the cylinder in the lathe, chuck the lap in the tailstock, apply a SMALL amount of lapping compound, turn on the lathe about 200 rpm, and by sliding the tailstock back and forth move the lap in and out of the cylinder. Tighten the lap slightly as it wears, add a little light oil as the lapping compound dries out. If the lapping compound seems "worn out," clean off the old before applying much more, as too much lapping compound contributes to getting a bell-mouth hole.
When you have a decent finish in the bore, stop, wash out the cylider well, measure the i.d., and turn down the piston so it's about 1/2 thou oversize. Lapping is not for removing a lot of metal...2 thou is way too much allowance.
You'll need to make a ring lap out of a disk of aluminum to finish the piston o.d. A question comes up here...how big is this piston? I'll assume it's about 1" dia, just for discussion. Bore a 1" dia. hole in the center of a disk of aluminum maybe 1/2" thick and 2" dia. Slit the disk nearly in half, and drill/tap for a screw so you can close up the slit. If you can counterbore this screw so it doesn't stick out, that will be extremely Good.
Set up the piston in the lathe, again turning around 200 rpm. Apply a small amount of lapping compound, wear a heavy glove (!), and by hand, work the ring lap back and forth along the piston as it turns, adjusting as necessary. Pay attention to what you're doing here, and be really careful that the lap doesn't seize on the piston, which could lead to some injury.
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