Unfortunately, their claims are completely false. Heating a salt lamp with a light bulb produces the same effect as heating a clump of table salt - nothing. While salt is certainly composed of positive ions (Cl-) and negative ions (Na+) arranged in a crystal lattice, turning on a light bulb cannot possibly dislodge the negative ions, since they are strongly attracted to the positive ions. Even if some ions become dislodged from the crystal, remember that salt contains equal ratio of positive and negative ions. The effect of any negative ions released will be neutralized by the positive ions.
Often, sellers will also claim that Himalayan salt is "natural" and different from table salt, which is "unnatural." However, Himalayan salt and table salt are both sodium chloride (NaCl) and are chemically identical. (The age of Himalayan salt also does not matter. 400-million-year-old NaCl is still just NaCl.)
And positive ions are not all bad. For instance, Na+, Ca2+, K+, etc. are essential for cellular function. "Positive ion" is just too broad a term to be applied in this manner.