I have one but don't know the thread. I presume it's because you broke it?
If it is because it's broken, take the bits out of the hole & measure the thread with a thread gauge, or measure the thread on any of the fragments you can get out. As a temporary measure, you could carefully drill & tap an acrylic sheet cover over the hole, seal with silicone, allow to cure & fill to the centreline with oil. This would enable you to use the lathe to make a replacement measured from the fragments.
If you use acrylic bar to make the replacement, be aware that acrylic bar available in this country is usually extruded & has built-in stresses that make it crack (if not immediately, then eventually) when machined. You can anneal the acrylic by simmering in water on the stove top for 30 mins per inch in diameter and then allow to cool in the water off the stove. Once done, the acrylic won't crack. Alternatively buy clear cast acrylic bar (virtually unobtainable in the UK – I have looked for pen making).
Regards,
Richard.
Edited By richardandtracy on 14/08/2018 12:17:47