I discovered the hard way that sanding on a lathe can be hard on the fingers. Now, to protect my fingers, I cut the fingertips off a latex-dipped work glove and wear one or two of the fingertips while sanding. Not only does this protect my fingertips, it also makes it much easier to hold onto the sandpaper.
I found a pair of these gloves at a hardware store for about $4, or you can order them. Caution: Don’t wear the whole glove while working on your lathe. You could be seriously injured if the glove got caught on your turning project or lathe.