For the purpose of elimination, would Barry explain how he changes gear please, both now and in the past? The symptoms could be explained by either forcing the box under power, or by a mechanical problem, or by a failed tooth due to earlier damage such as absently mindedly changing gear at high-speed.
Also, is it just the obvious missing tooth and other mangling in the red box, or is there a problem with the gear in green as well?

Lots of possibilities still:
- Operator error
- Faulty gear causing tooth to detach and get caught at speed
- Whatever caused stiff selecting broke and fell into the works.
Unless the gear was cracked during manufacture, it would take a fair amount of force to break a tooth and do the other damage. Only the lathe motor at speed plus centrifugal energy stored in the chuck would be powerful enough to do that much damage I guess? I don't think it would be possible for the operator to break teeth by turning the gear selector knob on his own. But maybe a damaged gear when the lathe was built has gradually worsened over time.
Would missing or damaged circlips or a faulty selector explain the damage? Maybe if the gear pair was run with only their very edges engaged, but wouldn't that damage both gears?
Where's Sam Spade when you need him?
Dave