It's deeply unfortunate that the parental attitude towards tools these days is never "learn to use it safely" but rather "Hide it away! Don't you dare let MY kid near filthy manual labor!"
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.
Otherwise lathes aren't more dangerous than any other piece of machinery with exposed moving pieces. In particular the ones designed to turn small pieces of wood can't do much harm.
Don't leave the chuck key in, wear eye protection, no loose hair, no loose clothes, don't be stupid and you will be fine.