Badger rings are not to be lapped, according to the owner of Badger Marty. This will cancel the warranty. Obviously.
That said, a lot of guys do.
Boomholzer has made some good points too. I never have lapped Badger rings or bedded a Badger rail. Never had too.
Standard rings with a 40mm scope will probably work. Are you going to be using Butler Creek caps?? I would email Marty @ Badger or call to make sure.
My USO SN-3 has a 44mm objective, with an ERGO parallax adjustment, BC caps, and I had to go with mediums.