You can get hurt standing BEHIND someone using a lathe. It used to be a common practice to use parallel bars to set material square in a chuck, but you had to remember to remove the bars before turning it on. Lathes in shops used to be arranged so you never worked inline behind another lathe.
I know of one guy that was killed on a very large engine lathe operating at a slow speed. His lab coat got caught in the leadscrew and it dragged him in and he was basically beat to death with the lathe chuck. There was no one close by and it was not noticed for hours.
You can also get hurt in CNC milling machines as well as CNC lathes that have the door lock mechanisms bypassed. There are precautions to take, but avoid going into or reaching into a CNC machine if it is in operation.
I've been in the business for 27 years and have had some cuts on my hands, but that's about it. I've never been cut by a moving tool, only by tools that were at rest or from sharp edges on parts.
Bob