For small stuff, I just stick a pencil pneumatic die grinder into a tool holder.
For larger stuff, eBay is full of tool post grinders, mine cost about $200.
https://www.ebay.com/sch/i.html?_from=R40&_trksid=p2499334.m570.l2632.R2.TR4.TRC1.A0.H1.Xtool+post+grinder.TRS0&_nkw=tool+post+grinder&_sacat=11804
Keep in mind, when grinding, take very light cuts.
Typically you don't want to take more than .0002" per pass.
Not a miss-type, that is 1/5th of .001".
And on small lathes, with a mini tool grinder, even that may be too much, due to flexibility of the lathe, and grinder spindle.
So just breath on the feed screw, and take multiple passes without feeding in any more.
You will be able to here when the grinder motor frees up, then just breath on the feed screw some more.
Otherwise you will probably just stall the grinder, or end up with chatter marks on the work, or a very uneven finish.
Honestly, I don't think a mini-lathe will handle it.
But you will find out.
Good luck....