Boo
I'm no lathe historian but loads of old lathes had odd size spindle nose threads, the only one I know off the top of my head with 1"x8tpi is the very old Atlas 6" and I believe that changed mid fifties.
If it is that size though it is a fairly common woodworking lathe spindle size but I can't see why they would want a 3 jaw (although I'm no woodworker). Also a lot of the early "import" lathes had various size spindles depending on who was buying them, the most popular 918 was bigger at about 1.5" or 39mm (ish) so if it is reasonably modern it might be the smaller 7x series - just guessing here I have no experience of these machines.
One last try then I will leave you alone to do as you want, one of the things I did early on in my collecting was get rid of all the old "junk" as I only wanted to keep the best (I like shiny new kit) and didn't like all those dark brown and worn bits about. This was a hard (expensive) way to find out that these things would have been very useful. When Fred/Bert whoever from up the road brings his piece of junk for repair (don't think you won't get asked) I hate loading it into my nice shiny new Bernerd particularly when it turns out to be a rough casting or some super hard material that is impossible to machine. Even worse is when a (close) friend just wants to do a "quick job" and then asks for a "bit of pipe" to do up the chuck properly!!
I know you won't see it now but there will be plenty of times to come if you use the machine seriously when an additional "old" chuck will be a godsend. I certainly regret having dumped several old Crown 3 jaws for about a tenner each when they could have saved my =A3150 chuck some serious bother. Unless you are lucky enough to get two village idiots bidding then if someone on Ebay will pay you a reasonable amount for it then they might also have learnt this lesson?
Hope you don't mind me trying once more to convince you - wish someone had told me. I'll let you get on with what you want to do now.
Best regards Keith