I have successfully made screws for a lachenal, the originals seem to be 42 to 43. Tpi my 1940 lathe could manage 44 which is close enough as thin as the “nut” plates are. You need to make a tool that supports the thin shaft as you turn it, otherwise it bends and you get a conical screw!
the similar fixture with a vee tool holds it while you cut the thread.
you need to cut the thread in one pass.
I had to round the tool just a little, the sharp vee was just too much of a stress concentrator, and the first ones broke too easily, looking at the originals Lachenal made the same discovery the bottom of his threads are rounded.