your household temperatures and humidity are within reasonable ranges and don't usually make a difference. The most important factors are correct watering of the pot, and correct (enough) light. I don't know palms, but Will or others can advise, best with good pictures.
I am worried the lizard light is a lot better making heat than light, and can't be close enough to the plant to help it a lot. Maybe you can change the bulb for a cool light, like LED= but better, find the right natural light.
