I've had several friends who do lathe work (Lefty, John "the Claw", Stubs) and none of them ever had a problem. They seem to be as safe as any tool, as long as you follow the basics (pin your hair back, safety glasses, don't grab the wood, etc.). I'd pop over to his house and give it a try first.
Good luck.
Bill
P.S. Those names were my attempt at a joke, if no one got that.