According to my chart They do make a barrel for the Thompson Center White Mountain Carbine. #910115 which is a .50 caliber 21" barrel with a 1-28 twist.

They only Lyman rifles I see barrels for are the Trade Rifle, the Deerstalker, and the Investarms Hawkins (Cabela's Hawkins).

You could double check with them. Call Kerry at 1-603-447-1095. She will be more then glad to answer your questions....