So has he only been tried on antibiotics rather than any antihistamines to see if it might be an allergy?
I've had swollen lips and they gave me antihistamines and a lady in Boots recommended some really good lip stuff to make them less sore as they got all dry as well.
Is he mentally sound, just in case he could be doing something which is aggravating it like things being too hot or even biting or chewing them in the night or a problem with dentures?
Does he have any other medical conditions and is he on any other medication?