Whittle a pencil down. Stick it in the hole and rub it on the threads. Then,check the pencil with a thread gage. Not hard to do.
If it's an odd thread,turn out the missing handle on your lathe. I have never NOT been able to make threaded parts to fit 18th. C. parts that were missing threaded pieces,even left handed.
Don't take the threaded part out of the chuck. repeatedly try screwing it into the hole and sneak up on it till it screws in. That is the simplest way to do the job rather than trying to figure out the actual diameter of the needed thread.