A worm has straight-sided teeth, it is just a screw thread with a shallower than normal thread angle. (In fact for a 14.5 degree PA the profile is the same as an Acme thread (14.5 degree half-angle) though the tooth height etc are probably oddly proportioned for the diameter/pitch. It is unlikely that you have a lathe that can single-point your worm using an Acme insert, though.
If you have ever wondered why the threading table on your lathe includes MOD and DP pitches, this is why. It is so you can cut a worm thread to suit a standard gear tooth pitch.
This assumes a non-enveloping worm and wheel, things get more difficult if the wheel isn't straight-toothed, you need a cutter with the same radius as the worm, or a machine that can generate such a curve.
(Ponder, I haven't thought about that before, but my CNC milling machine in hobbing mode can probably generate wheels quite nicely, except that most of my hobs are bigger than any worm I would be using)