Pain in lower eyelid cuz of eye cyst?

Probably Stye: If this occurred rather suddenly, it probably is a stye, which is a blocked oil gland of the eyelid. It can become secondarily infected and can spread to adjacent tissues leading to cellulitis. Most of these styes respond to very warm compresses 3-4 times/day for 10' followed by gentle massage with a washcloth containing a small amount of baby shampoo. After a week, the stye should nearly resolve.

Chalazion: The most common condition causing pain in an eyelid associated with a "cyst" is a chalazion or "stye". Treatment is with warm compresses as often as possible (at least 4 times a day for 5 minutes). If it doesn't get better see an ophthalmologist.