+1 for a Tangential tool.
The expensive way is to buy. The cheaper way is to make your own. Also you can choose the size of toolbit, and make the holder to suit your particular machine. I am not a precision engineer, but my home made ones work well.
All that you then need is a simple jig to hold the toolbit for grinding.
If you have not seen a drawing, it is just a rectangular piece of metal with the under side machined at 20 to 30 degrees. Imagine a wide wedge.(Opinions vary as to the optimum angle, but over this range the tool is effective) The upper side has a vee groove in it, at right angles to the long edge of the angled side. On this upper surface drill and tap two holes for clamping setscrews. The upper part of the clamp is merely another rectangular bit of metal, thick enough not to bend when clamped, with two clearance holes on the same centres as the tappings in the base.
To sharpen the toolbit, place one corner in the Vee groove and clamp it using the two setscrews. The toolbit is now held at the correct angle, and can be ground by rubbing gently along the side of the grinding wheel.
The cutting edge will be diamond shaped.
Once sharpened, set the cutting edge to the centre height of the lathe. (if you have not made one already; make a gauge to set tools to centre height. It will save a lot of time over the coming years). With the holder square on to the lathe axis, you have a tool which will face or turn without any change, and produce a surprising good finish, whilst being able to take very fine cuts.
I have used mine for cut depths ranging from 0.0005" to 0.050". For fine cuts it is advisable to resharpen the toolbit and reset it to centre height.
Howard