I have moles in my eyelashes, Can I be put under anesthesia for removal or does it have to be a local?

Best option is to have a dermatologist evaluate the pigmented lesions. Sometimes people develop seborrheic keratoses on the eyelids, and those may be treated with cryotherapy. If the lesions are nevi or moles, they can also be removed with local anesthesia. If you truly want general anesthesia, I'm sure the dermatologist can discuss this with you and if necessary refer to a plastic surgeon. But the first step should be to see a dermatologist and have them evaluated. Good luck.