I am embarrassed to say that I line the area under my lathe with a sheet of 4mil plastic sheeting. When I'm done, I pull the whole thing out and dump it. A new one goes in and I'm ready for the next job.
Yes, hot chips dimple/melt some of the plastic but it catches 99.9% without leaving any in the tray and my paint is totally intact. Call me stupid but it works for me ... and it works with aluminum, too!