From the LMF website;
To finish the barrel, heat the surface with a torch until it is too warm to comfortably touch with bare hands, about 125 to 130 F. This will drive off any remaining moisture. Next apply a liberal coat of motor oil. Allow the oil to bond with the brown for 24 hours and then polish off any excess with a soft dry cloth. Apply a final finish of a quality gun oil, non-abrasive furniture wax or neutral color shoe wax.