Buy or make a nut to hold in the jaws. Use another as a jam nut to secure. Collet would be perfect. If it is a true lead screw and has Acme or Square threads don't worry about it. Hold it in the jaws and go easy.
just bore a hole in a short bar of aluminum, the exact diameter of the thread OD.
Then saw a slot through one wall, and insert the screw.
Close the 3 or 4 jaw chuck on the aluminum, it will clamp the thread as true as your bore!
Then you can machine the ends to suit your needs!
Check the thread " Manual to CNC lathe conversion. I have pictures of exactly what " Widgitmaster" has explained above. It works, its safe, its accurate.
If the material is hardned all the way through you should use a 1/64 radius cutter with a little positive rake, such as a CMNP or CNMG carbide insert,this will give you a good finish and decent depth of cut.