The keyways with the teeth and the worm gear on the sliding blocks that are engaged in/on the teeth . ( jigs I'll call them for now )
I think they are to keep whatever us being lapped in ..... in the same plane ie. no accidental or unintentional rotation .
It would then be a simple exercise to lift off & rotate the lapped part/s & set them back on the " jigs " either through 90 , 180 or 270 degrees to get a decent flat polished lapped surface .
Lapping in like that would be about the quickest & most accurate way if your doing it by hand .
The criss crossed diamond groves will most likely be there to allow fine ground off debris & the used lapping paste to fall into them as quick as possible to stop it causing problems on the metal plate & whatever is being ground /lapped flat . Think jewelers rouge for the lapping paste , it's just a really really fine grit & some oil .
Perhaps see if you can find info & pictures for a lapping plate for optical quality glass prisms , possibly for use as military tank / armoured fighting vehicle periscopes or the mechanical range finding binocular type devices / scopes that were in use till the 1970's or so before TTL & digital electronic technology replaced them .