Gross alignment is no big deal with rubbing stones together but I would get a plate of glass, initially, and test it for cohesion with the stone. Then add some more lapping on the glass with wet/dry sandpaper, until you attain strong cohesion.

I'm concerned about lapping a stone with dry "wet/dry" sandpaper. Although I'm not expert on any of this, perhaps that isn't the best way to do it. I've certainly never done that. Did you read about doing that here?

Make sure you remove all the grit now embedded in the stone.

I agree that the lower grit cuts will not be a big problem. But good lapping wouldn't yield them, to me they seem to be an indicator that the dry lapping isn't such a good idea.