The college that I went to had all the engineers learn how to run a metal-turning lathe. ME, EE, BME, I think even the Computer Engineers had to learn how to run a lathe. They put us through a safety class first, which mostly consisted of how not to run a lathe (no loose clothes, no long hair, no jewelry below the elbow, no necklaces, etc). The only injury that I know from that class was from when we learned how to run welders - one of the guys caught his shirt on fire with an oxy-acetalene torch.

Yeah, lathes are dangerous, but no more or less dangerous than a lot of other things in the world. Cars are dangerous. Turning on a light switch in the wrong context can be dangerous. If you approach this stuff with the proper respect and caution, you should be fine.