you can simply wet the back of a piece of wet/dry sandpaper of your choice and stick it to the surface plate.
you then can lap until you can't lap no more.
when you are finished lapping, remove the wet/dry sandpaper and put another on for the next operation
I think that is called sanding - or at best honing.... the results are flat within microns at best. Lapping is at least one order of magnitude finer. The results are measured in fractions of wavelengths of light....