You could try asking Axminster. You might also win the lottery.
Can the person who owns the lathe make an imprint of the spindle thread (using polymorph mouldable plastic or similar). Then you can cross section it and measure the thread form.
Alternatively, make the person a triangle with a 55 degree angle, a 60 degree angle and cut off the 65 degree angle. Ask them to see which fits best (push the template into the thread vee and shine a strong light behind it).