I also use a Lyman, and it is excellent for cleaning cases up. Use a Corn Cob media, with a couple of caps of a polishing agent - normal liquid brasso does the job a treat....
Adds a bit of time to reloading, but there is no rush, I do mine in batches, and using nice shiny cases to turn out your rounds is satisfying.....
Also, a benefit is that if you re-use the cases, having them cleaned up makes the inspection for wear that much easier. Bin any cases that are not totally sound.
All the best. Neil