Could be chatter or metal-on-metal or... ? Does sound like it's time for new shoes.
Depending on the condition of the cast-in-place brake drum, it may be ok for use after a good cleaning and refitting new shoes.
Turning the brake drum is problematic for several reasons; finding a shop that can secure the entire rim to the lathe equipment, and if too much metal is cut away, the arc of the new brakes shoes will no longer fully contact the drum.
Encourage you to park the bike until such time as you can do a through inspection.