Tim.
When precision barrel makers lap a bore it is not done to smoothen the bore, that is only a secondary consideration since the barrels are already smooth.
Lapping is done to bring the barrel to the exact required dimension and remove any inconsistencies. The machining of either Button rifling or cut rifling is kept slightly undersize since this process can't achieve exact dimensions, specially when stress relieving is requred.
Hence the expensive barrels are lapped to size and uniformaty and to remove any tooling marks. The lap is rotated every 4-5 strokes. After some lapping a new lap is poured until the finasl dimenion is achieved. A lap is not just a lead slug, but poured into the bore and is about 4-5" long. We are talking match barrels. Lapping is the work of an artist.
Just for the record, what is being done on a Handi is not lapping but polishing. Just from what I have seen with a 22x bore scope on several button rifled Handi barrels, is that they are very smooth, excessive polishing will do more harm than good because of the shallow grooves. Consideration should also be given to proper terminoligy for new shooters.
Shoot and clean for 20 rounds will put a Handi barrel in service.
Many of the fine rim fire barrels get a choke lapped in of about 0.0002. Bill Calfee of PS Shooting will attest to that fact.