We had a metal lathe in our high school shop class. I still can’t believe someone didn’t kill themselves on that. I think wood lathes are fine, but honestly that should be kept out.
They run at high speeds, the workpiece is typically less secure, the material has a grain structure prone to catching the tool and digging into it, ventilation is required, and most importantly, the cutting tool is gripped in the operator's hands instead of being secured on a toolpost.
I'm not real comfortable around lathes.