I have a meibomium cyst on my lower eyelid. Dr said it should go in couple of months. 9 months later and I still have it, what should I do?

Open and drain. If it is bothering you it can be opened and drained or removed in a five minute office procedure. Otherwise there is no harm in leaving it alone. I assume you have used hot compresses four times daily as well as a mild antibiotic drop at acute onset already. If not, that is still worth a one week trial.