Do salt lamps really produce negative ions? Do you know about any scientific study that could support this assertion or disprove it?
There is no study because there is no physical mechanism were a salt crystal sends negative ions into the air without any energy input. Just heating the inside up with an incandescent lamp warms the lamp a bit but this does not create any measurable amount of negative ions.
There are ion generators but these work on a completely different principle. Basically you need a very high electric field to ionize air molecules or dust particles. Here is a study that explains how the air quality is positively influenced by a air purifier that creates negative ions.
This website addresses this issue. I have no idea how rigorous it is but it is interesting. http://www.negativeionsinformation.org/saltcrystallamps.html