What is the fuse (that blows persistently) wired to? (both schematically & in real life)
When the lathe zonked, was it during actual cutting, or when a switch was thrown on/off?
When you temporarily rigged power to the motor, does it just turn or will it spin to full rpm? (not sure that's possible to check safely without the speed control thingy in line, but just a thought).
There are diagnostics for checking motors across various windings, but above my pay grade.
I think its worth examining those switches too. If there is a partial or intermittent short for whatever reason, then current can go where it doesn't belong. Is it relatively easy to pull them out a bit to examine the wiring connections? Ideally remove switch altogether & test contacts with continuity meter? If you see loose tabs, melted plastic or evidence of magic smoke that would be suspicious.