I don't usually lap barber hones unless they are really dished. IME, years ago, barbers didn't lap them. I think washing them with a nylon bristle brush and trying them is your best bet. I lay a straight edge on them to check them first. If I do lap them I used to use a 325 diamond plate but went to 120 (DMT D8XX) to save a lot of time. If I was going to lap a barber hone with sandpaper I would start that low and work up to get it smooth as possible. 1k sandpaper would be as high as I would go. YMMV.

The hard black ark has been good for me with an already shave ready razor. Improving the edge I mean.