To get a nice, even grind on the outer circumference of a socket, get one of those socket adapters that convert 1/4" hex drive to 1/4", 3/8", or 1/2" square drive. Put the hex part of the adapter in a drill, attach the socket to the other end, and run the drill at a low, constant speed as you hold the socket against a grinding wheel. Maybe not as good as a lathe, but infinitely less expensive and usually produces a socket with a pretty uniform wall thickness.
I’ve made a complete set of ‘thin wall’ sockets out of middle-of-the-line tools and have yet to have one fail, and I’ve put quite a bit of torque on some of them. Twelve point sockets have a more ‘round’ ID configuration, and thus the outer wall can be ground thinner than six-point sockets without sacrificing structural integrity.
I used a vibratory engraving tool to re-mark the size of each socket to avoid guesswork. I couldn’t tell you how many times I’ve used this set of sockets. Over and over and over again, they’ve saved me time and frustration with bolt heads that are just too close to surrounding components to use a standard socket. The walls are thinner than the thinnest ‘thin wall’ socket and still work just fine.