One claim is it adds negative ions to the air which the claim is are good for you. There's no evidence they'd release anything more than an infinitesimal amount. Salt is pretty stable.

Another claim is it helps purify the air by trapping toxins, which, even if true, would quickly become useless as the surface area becomes saturated. There's also no evidence any pollutants end up on the lamp beyond pure coincidence/chance.

The heat makes the lamp atoms vibrate at a higher frequency, which in turn makes it deteriorate. To maintain its structure the lamp seeks out emotions vibrating at other frequencies to pull within itself. Drawing these "Bad Vibes" into the lamp is what makes it salty, and a naturally gifted or properly trained Empath can taste this salt to see what has been absorbed by the lamp, to gain knowledge of the owner's troubles.