Lapping is a very accurate process it is how very precise surfaces are produced. IE surface plates, gauge blocks, pins most precision tools.

You can "grade" your own lapping compound from grinders dust from a pedestal grinder or surface grinder with just 2 clear bowls and some water or light oil.
Put the light oil water in 1 bowl and sprinkle the dust on top let sit very still for 10 mins then carefully drain into other bowl. This sediment layer is normally 2 coarse for most work. continue letting the bowls sit and draining each time the sediment is finer and more even.

As you lap with compound it will slowly break down into finer grits thru natural wear. I normally dont add more compound just water or oil in small amounts to jeep the work wet and flowing.

Working a sizing die will go fast as the actual surface area is very small in most. This ring inside is what is doing the work, Very similar to a burnishing tool.

Even on the nitrated dies if you do break thru the thin hardened surface the 12l14 core is much harder than the lead and will last a long time