It's hard to find an miniature internal threading bit that will do less than about a 3/8 hole.
You can grind one from a very small HSS boring bar, but with bores that small it is a really touchy operation to do the threading this way.
Doing an external thread on some appropriate sized drill rod then carefully filing flutes into it will usually make an adequate small threading die for softer materials, heat treating it after getting the final shape finished will make it last for a long time unless you're trying to thread something hard (a MAPP gas torch is best if you don't have an acetylene rig available, but very small rod can usually be done adequately with propane). Heat treating it is really a very simple operation, just heat it till it becomes non magnetic (something close to yellow hot depending on how you see the colors), hold it there a minute or two, then quench it in the appropriate media (Oil for "O" rod, salt water for "W" rod and simple air cooling for "A" rod).
I should mention, if it's a standard thread you can also make a soft material tap out of the right sized grade 8 bolt (but you don't get to play with the lathe as much that way, not to mention the yellow hot steel). Look at some self threading bolts to get the basic idea then experiment some.