The best answer is, of course, to not use the lathe at all. A dedicated polisher is easy and cheap.
Mine is salvaged from my old furnace blower. A Harbor Freight arbor (less than 5 bucks) attaches to the shaft to allow buffing wheels (also HF) to be used and changed out quickly and easily. The motor is mounted to an old sewing machine cabinet (roadside pickup) such that the wheel extends out over the edge of the top to give me maximum clearance. A piece of old carpet taped to the wall catches most of the debris, and pads the surface for the inevitable flung parts.
This has several benefits. The first is, obviously, safety. No spinning chuck jaws to catch a knuckle. The second is to keep all the mess away from the lathe. The last is to have multiple wheels for each material, and each polishing compound. I write directly on the wheel what it is for (brass, steel or aluminum) and I have three grades of each one. Polishing compounds are stored in the cabinet drawers, as are the other wheels. Also in the drawer are an old file (for cleaning the wheels) and a wrench for changing them out.
This polishing stand also has the bench grinder mounted to the other side. This keeps all the grinding/polishing mess in one area, away from the lathe and mill.