Its a good idea frame your lap; 1] to attach paper retainers 2] provide means to secure the plate to a work surface 3] reinforce plate into a dependable plane.
If flatter yet is desired, use 3 plates to cross check intended plate. Glass or marble will respond to loose abrasives in water or oil slurry.
Working 3 plates is THE classic method of producing true flat. Unsure who created it but an early important use was by Joseph Whitworth. They didn't have means to measure how flat, but it was later realized he was attaining millionths ~.000005 or better.
To lap parts correctly, the part hardness should exceed that of the lap. The abrasives work by embedding themselves - 'charging' - the lap. Interpreting something like Moh's Scale will show glass harder than metals in general. Grooved cast iron is very common material for lap plates and certain cylindrical applications, but copper and soft steel show up in more hole laps than iron.