True!
The mantles (nets) contain silk/cotton/nylon impregnated thorium. As a high temperature oxide, thorium oxide is important for the stability and function of the mantles. As thorium is present as an isotope (232Th) that is an alpha particle emitter, be very careful around the dust from a broken mantle! Don't take a deep breath to blow away the ash; it is a great way to suck radioactive particles into your lungs.
Needless to say, the exhaust from a gas mantle contains a few thorium particles, and is therefore radioactive, so using one in an enclosed space isn't ideal, and as the lanterns are also sources of carbon monoxide, there is another reason not to use a gas lantern in an enclosed space.
IIRC: Aladdin made a version based on a kerosene wick lamp that was stunningly brighter than a normal kerosene lamp, and required a rather tall glass chimney to get enough draft.
Gypsum, e.g. drywall, is radioactive for the same reason and a major source of radon in tightly sealed homes. Gypsum contains uranium as well as thorium, and both decay to radium, which decays to radon.
Phosphate rock contains the mineral phosphorus, an ingredient used in some fertilizers to help plants grow strong roots. Phosphate rock contains small amounts of naturally-occurring radionuclides, mostly uranium and radium.
www.epa.gov
Don't forget "blue" tungsten TIG tips, some of which contain a fair amount of thorium (2%), which you want to be very careful not to breath the dust, and contain any dust from sharpening. I never understood why some welders thought it was safe/smart to use a powered grinder to sharpen blue tungsten as it sends thorium everywhere.
The health risk with thorium dust in your lungs is that is an alpha emitter. The particles don't go far, but the alpha radiation is enormously damaging to cells in general, and the delicate tissue of lungs in particular.
All the best,
Peter