Joe, Whats the spindle bore on your lathe ? if you can get a bren barrel in and fit a spider chuck or similar on the end of the spindle then you can drill /bore the original barrel, you need to make up a drill with extension, to get an idea on tolerances and heat required try a small example.

If you can freeze the liner too it helps....

Cant say I've done a Bren barrel , but relined a few .303 Enfield barrels to .22, very similar to Peters advice. the last one I did I used an unfrozen liner instead of the one that had been in deep freeze over night, all going well until the last 1/2" had to revert to the hammer managed to get it in but just..... I left plenty of meat on the chamber end just in case.