To my great surprise, personally I've always had more problem with boring (big holes) than with parting off on my Chinese mini lathe - definitely NOT the most rigid of machines we'd all agree!
I use a very thin (perhaps 3 mm or less - HSS) tool in a holder from the front as "normal", mounted in a QCTP. I make sure to get the absolute MIN overhang possible, make sure the tool is set EXACTLY at 90 degrees to the bed, is SHARP (with a TINY round over at the very tip - very fine diamond file/lap), and make sure it's set at EXACTLY centre height. I set rpm by ear, not too fast (no rev counter on my lathe), and a "not too aggressive" feed in.
I use lube with nearly everything, WD40 or paraffin on ali, a synthetic cutting fluid with everything else.
To my VERY great surprise (based on all the reading I'd done, and the minimal turning I did during apprenticeship) I expected big problems, but it's all gone very well indeed and I've never had a problem/broken a tool (as above, as opposed to when boring).
One tip I did pick up from one of the Mini Lathe web sites a while back is that using such a thin tool and when parting off a fairly big dia work piece, it's best to start the first cut just on the waste end, then when about halfway through, start a second cut overlapping the first, but this time with the tool set to the part off length required.
Although in cross section the tool is slightly narrower/thinner at the bottom that at the top, when going into a deep slot (which is how a parting off job starts out after all) you can get some binding between the sides of the tool and the work piece, The 2nd cut eliminates this possibility (or has for me so far anyway).
As said, I really couldn't believe just how easy I found parting off to be
- really a genuine case of jammy blind beginner's luck.