This stuff is the same as the acrylic pen blanks. It doesn't normally produce dust when turned. If you turn it slowly enough you can get away with a gouge, with similar results to a scraper (see below). At higher speeds, the material splinters into small chips a couple of millimetres across - way too small to be a lung hazard.
A sharp scraper though will produce incredibly long shavings - unlike wood, the plastic is resilient enough to hold together laterally (not being fibrous), so the shavings can be yards long. They are thin, long, and wrap around the lathe, the tool, the tailstock, and anything else. Did I mention that the shavings get very long?
Again, these are not hazardous.
There could be a dust problem from sanding, where the particles are just as fine as with wood, so this is the time to use extraction and/or a dust mask.
