Lathes need more extraction than almost any other machine, because they produce all the extremes. Largish chips right down to dust so fine it cant be seen, and perversely, the harder it is to see, the more it floats and the more dangerous it is.
Its best to have a large extraction hood at the rear of the lathe, and a fresh air supply from behind you blowing the dust towards the hood. Many makes, endless home made versions, but make sure you dont let it slip by you.
Even then, WEAR A MASK! You only get one set of lungs (transplants excepted) and you really dont want to be unable to even walk without gasping for breath.
And at the end of each day, vacuum the place out. Do you have kids? would you want them wandering around kicking up clouds of harmful dust when they come to see what youre doing?
woodworking can be very hazardous if you get lazy.