It is branchial cleft cyst and nothing to do with your lungs. It is rather associated with a congenital anomaly that occurred when you were a foetus developing in your mother's womb. It now needs to be removed before it causes more problems to you. It has nothing to do with your sexual health, fertility or vitality.
Next Steps
Go ahead and get the surgery done. If your Surgeon is competent enough to diagnose this, he/she is definitely competent to operate upon you! Please give my regards to your doctor and wish you a speedy recovery.