You can thread a blank screw with just a die and handle, you don't need a lathe. You can even use a larger and longer screw and a drill press and file to remove the threads, trim the head to the right diameter, and shape the head. Then you grind the sides of a hacksaw blade to thin it to the right size and use it to cut the screw slot. The last step is to cut the screw shank to the right length. Sounds like a hard job, but takes about 15 minutes.
If you can determine the screw size, you might be able to use a standard screw, but in the days before national standards, most gun makers made their own screws to whatever size and pitch they needed for the job.
Jim