Wood shaving and lathes go hand in hand, but your turning tools don't need to be part of the mess with this "off-the-shelf" solution.
Lathe with tool shelf

I like to have my lathe tools close at hand, so I found a way to mount 12"-wide wire closet shelving to my lathe stand. The plastic-coated stuff is available at every home center, and when installed upside down, it keeps lathe chisels from rolling off the shelf.

After finding where the front-to-rear splay of the legs of my stand equals 11 12 "—the distance between the outer bars of the shelving-I marked that height on all four legs. Then, I cut the shelving to the length between those marks, leaving an extra 1" or so of edge bar and shelf-base bar on each end. On most lathes, you'll probably have to loosen at least one leg on the stand to slip the shelving into place. After that, gravity and the splayed legs keep the shelf in place.

On lathe stands without splayed legs, you could drill holes in the stand just underneath where the shelf will rest, and then insert 38 x1" hexhead bolts, nuts, and lock washers. The bolt heads will support the shelf ends.
—Bob Zajicek, Marietta, Ga.