Here is a simple way to grind small items on your lathe. I clamped the handpiece of my flexible Dremel extension in a Phase II tool holders and was good to go. In the picture you can see the center that I have just trued using the compound set at 60 degrees. The center was a bit chewed up, but it just took a few seconds to fix it.
I've seen other inexpensive jigs that have a threaded hole in one end into which the whole Dremel tool is screwed. The other end of the jig is clamped into a tool holder. These look like they would work well, but I already had the handpiece, so went that route.
Since the airgun parts I work on are fairly small, this idea should work OK for any grinding work that might be necessary for me. One application that comes to mind is making new Gamo pivot bolts to replace those that usually get boogered up (Texas technical term) in taking the rifles apart. McMaster Carr has a bunch of metric shoulder screws in different sizes that might include one that would work, but I don't have any in hand yet to check the exact fit in the Gamos. If any work on the shoulder diameter is necessary, the Dremel would leave a great finish. Certainly better than I usually get with HSS tools.
Use common sense around high speed grinding bits and protect the ways of your lathe from the grit produced by the grinding operation. If you shoot your eye out or otherwise maim yourself using this tip, consider that you were forewarned that the risk of using the idea is solely yours!
I'm fairly new to the machining hobby, so if this really isn't a new idea, my apologies to the original inventor.