Cysts on the edges of the eyelid can be snipped off, or they can be removed with something called a V plasty. The V plasty is an indelible removal method that is successful because it removes the root of the cyst. Snipping a cyst off, removes it, but growback is likely. However it does not require general anesthesia. In very old dogs, it is quite often the best choice. Always consult a veterinarian.