I built a tray for over top of my headstock from a thick plastic cutting board. But it hovers above the cover. When I needed to mount my dro unit, I used a tube that came with it, tabbed a bracket that bolts to the back of the lathe to mount the tube to. My tray pivots on that tube sort pivots out of the way enough the top cover can be removed, or access made to add oil in that fill hole. Yes, it's real handy to have the tray there and it holds all sort of stuff, a few hss cutters, carbide inserts, insert wrenches, mic's, calipers, a dead center or two, my compound wrench, small stuff like that. No qcth's there, they reside in a rack on the wall behind the lathe with the other heavier tooling. Then there's a collet rack next to that mounted on the wall. Heavier tooling is on a shop cart under my workbench. Everything within easy reach. And no, nothing has ever fallen off/out of the tray. I milled pockets in it when I made it, though it did warp in the milling operation. It just sits there holding tools for close access. It is cluttered though as flat surfaces tend to get. So I sort things out every once in a while to deal with the clutter. And it catches small chips at times.
Regards
Bob