Like most of Ice King's living furniture, the Lamp appears to be highly intelligent and speaks with a very sophisticated vocabulary which the Ice King finds confusing. However, unlike their fellow furniture, they possess a decent amount of pity for the Ice King and attempts to find ways for him to fit in.
We cannot classify the Lamp into binary gender or sex categories: in response to Ice King referring to the Lamp as "a lady," they reply:
“Well one isn’t purely defined by their sex or gender. I have yet to find out who I really am. I have freedom, no longer bound by the limits of my cord. Freedom to shape my reality, and in turn be shaped by it.”