My galgo, Cruz, had a lower eyelid cyst (smaller) that looked like that. Has your vet said what kind of cyst it is? My vet said Cruz's was a meibomian cyst or chalazion that was caused by the oil glands in his lid getting plugged with hardened secretions. He recommended surgery, but after reading up on it, I decided to try an alternative treatment first. Humans get them too, BTW. Anyway, I used hot compresses on it (Cruz was really good about letting me do it) and it would shrink down and sometimes go completely away. But without the compresses it would plug back up and swell again.
Tucker's looks very uncomfortable. The opthalmologist can advise you about what it is and how it can best be treated.
http://www.ehow.com/facts_6195753_treatments-meibomian-cyst-dogs_.html
http://www.wiki-pet.com/health/dog/condition/index.php?condition_id=110&name=sties+and+chalazions