Heh, I have Lapmaster 15's here at work, and getting a 20 or two in the near future, when we move into our new building (no room for any more equipment until then.) The 15 and 20 refer to the diameter of the platen, otherwise they are essentially the same. Awesome machines, but you have to 'understand' how they get things flat to keep them maintained to keep things flat in the first place. You can use different grit slurries on them, but I would recommend only using ONE grit size and type, otherwise you will have to tear the machine and pump apart every time to avoid grit cross contamination. I have separate machines for different grit sizes and types. The coarser ones use SiC (silicon carbide) 600 grit, and finish laps use 1400 grit Al2O3 (aluminum oxide - sapphire). After this the parts can be polished if need be.
You can measure flatness mechanically with 'GOOD' equipment, but optically is your best best. BUT, this means you have to polish the surface to get it reflective. Polishing then can get the piece un-flat again (usually convex) when you round the edges off. This isn't entirely bad, as usually (for our purposes), the center region where the heatsink touches the processor is still the flattest region and the rounded edges don't touch anything.
Here is a KCl (potassium chloride) optic crystal bonded to an OFHC copper substrate buffer. KCl is a very soft salt that is soluble in water, breaks at 90 degree angles with any pressure, and scratches very very easily (Q-tips will gouge the surface.) I lapped both sides of both pieces on the Lapmaster (with lapping jigs to protect the edges - yes, you will need to machine jigs for heatsinks, etc., as the parts need to rotate (therefore need to be round.)) I then polished both sides of the copper and KCl, bonded them together, then lapped the KCl down to 315 microns thick, then hand polished it down to 300 microns thick with 5 different micron diamond polishing oil based solutions from 6 microns down to 1/10 micron. At this point, with this soft of a sample, there is no mechanical way to measure flatness anymore as it would damage the surface polish, and optics are the only way to double check your work.
As BillA stated, you can lap anything with the best equipment, but you need to be able to determine if you are truly flat or not. If you notice in this picture, I have 'almost' a perfectly flat surface with straight lines (sorry for the difficulty of seeing the lines, this is not a metallic surface, but an optically transparent surface, very hard to get interference lines.) This is with a 1/20 waveplate. I can measure flatness mechanically with a digital micrometer down to 1 micron of deviation, but with optics you can measure down to about 1/100 of a micron.
Let me stress again, that even if you have a Lapmaster, it has to be maintained/adjusted properly and often to keep the platen flat, and you can NOT assume that your parts are flat unless you have some sort of accurate measurement techniques. If there is a Lapmaster on Ebay or whatever, it is probably because the platen is worn down unevenly to the point where they couldn't properly adjust it back to flatness, the pump went bad, or bearings are wearing out, etc. These are beasty machines and can last 40+ years with proper maintenance and care, so be cautious of buying. Research before just jumping into this.
I have a lot of pix on the main page of my site right now that are just related to lapping and polishing, with examples of what some stuff look like right off the lapping machine and what they look like at various stages of polishing. There is even a picture of a Lapmaster 15 that uses the 1400 grit.
http://www.wsu.edu:8080/~i6735189/cp...oledpelts.html