I grooved several dozen lapping plates over a period of years for an optics application. Flat lapping on Hoffman PR series machines.
I've got the gang of slitting saws still mounted on the horizontal arbor, hanging on the wall behind the mill.
Grooves are a necessity if you want to be able to control the lapping plates. And If a large bit of airborn grit falls on the lap, the grooves give it a place to go. No matter where you start, the lapping process changes both laps and the work. There is a need to play work piece loading, weighting, and speed along with slurry delivery to hold flatness.
Single sided lapping still needs a segmented plate for the stray grit issue, with the conditioning ring location doing the lap correction. Without an interferometer, You are guessing, or playing rough. I suppose a Talysurf could be used to check the work. but not as easily
