There are many threads on this but I wanted to share my own experiences and seek the wisdom of the Tribe of the Stone.
I just lapped my Nakayama asagi on 1200grit and 2500 grit wet/dry on a glass window pane in my apartment which pivots to lay horizontally. I've done this before, starting at a lower and finishing on a higher grit, but today I tried something new.
After a few pencil grid checks on the 1200 paper I had a nice puddle of mud on the glass window so, reflecting on the three stone lapping trick Jim and Hide have shared from their visits with masters of the craft, I lapped my stone on the mud puddle. Essentially, my stone lapped itself.
Just to be sure I drew pencil lines again and lapped on the 2500 grit, the lines disappeared very quickly with no pressure, so I removed the paper again and lapped on the remaining mud. The surface isn't as refined as it will be with repeated honings and nagura conditionings,but it is noticeably smoother than the sandpaper alone would leave, with no scratches.
All that said, I did leave scratches and a slight haze on the glass. I wonder if the landlord will notice. This brings into question the idea of using grits on glass or granite over time, but with what I have available this more than suffices for now.
I was even able to do that gliding spinning hone trick I've seen in videos, which seem to prove the stones are lapped as flat as can be.