I'm by no means an expert on machine tool use, but I have a couple of suggestions for using a tool post grinder on the lathe (If you all don't mind an amateur's input)
I know grinding on the lathe can be damaging if things are not protected, so here's what I do. It may be overkill, but why risk it?
Step One-
To protect the ways, I wipe them down if they are not already clean, then re-coat them with fresh way oil. It seems to be thick enough that any dust from the grinding stone that escapes Step Two (below) will be suspended in the oil. But, this is just my observation. Another, perhaps better product, would be Hyper-Lube from the auto parts store. it is really thick & sticky. Cleanup is tedious, however. Naphtha seems to work well after using sacrifice paper towels (or in my cheap-skate case; newspaper) to wipe it al down.
Protection Plan Step Two is to wrap the oiled ways with food service cling wrap. It is like a thick "Saran Warp" and comes in wide rolls. The sheet has some tackinesss to it when stretched. I just go 'round-n-round', circling the ways & chip tray, pulling tight. The stone grit seems to stick well to it. Any dust that escapes gets trapped in the oil on the ways. My roll is 20" wide. Restaurant suppliers and some shipping suppliers sell it. (Uline com 'Stretch Wrap")
The Tool-
I use a Dumore flex shaft grinder that I got at a garage sale. Sometimes I'll use a Dremel tool also, but it's shaft doesn't run very true. Of course, with either, there is not a great deal of precision.
The handpiece gets held in a homemade tool post mount. I stuck some pictures in this post.
One day, I'll find a tool post grinder begging to come home with me.
Like Tubalcain said in the video that Garage Guy linked, wear a face shield. Flying stones are evil.
Have Fun & Enjoy This Day!
Paul