Use alignment rods when you mount the rings
I bought some alignment rods for scope mounting years ago and they are great. Picture two rods each machined to a point at one end. Place one in each ring loosely tightened then bring the points together to verify the rings are exactly true to each other in alignment. Lapping uses a different kind of one piece bar that goes through both rings at the same time. Loosely tighten the lapping bar with lapping compound on it. Moving the bar back and forth will then "lap" the two rings round de-burring them. I think you would want to lap them only after verifying that they are in alignment first.