Hello bluemoon1,
Bert is absolutely correct. Common salt, that is sodium chloride is hygroscopic but not deliquescent. It might be that there is an impurity in your rock salt lamp that is resulting in the deliquescence you are observing. Calcium chloride would do this, and could well be present if your lamp is made from 'fake' rock salt. In any case I would not suggest that you taste the liquid as calcium chloride, if present, could burn your mouth chemically (with no disrespect to Bert's answer).
Regards
Peter Jameson