You're airbrush is probably OK.
The term "mineral spirits" is usually interchangeable with "paint thinner" and "white spirits." They're are good for thinning enamel paint and cleaning up afterwards.
Lacquer thinner is a different mixture of chemicals altogether. While meant to thin and clean up lacquer paints, it is also strong enough to clean up/cut through enamel and acrylic based paints. Mineral spirits, on the other hand, generally aren't strong enough to cut through lacquer-based paints.
All airbrushes I know of can handle lacquer paints and thinner. If anything, you might have constricted the airflow a bit by allowing lacquer deposits to build up when the mineral spirits wouldn't remove them, in which case a run through or soaking of lacquer thinner will probably remove them (if you're going to soak, remove rubber/Teflon gaskets first). But if your brush seems to be working OK, it probably is.