As other plastic surgeons have mentioned, you may consider being tested with other anesthetic solutions to determine allergy. You will require more anesthesia beyond any topical cream for any face lift surgery.
A face lift is not one operation, but rather many potential operations dependent on the surgeon and patient to improve neck line, jowls, and facial aging. Typically most have face lift surgery on either IV sedation (twilight anesthesia) or general anesthesia. Either are good, safe options, with their own advantages and disadvantages. Some facial plastic surgeons perform face lift surgery under local anesthesia. Anesthesia may be provided by a board-certified anesthesiologist and/or nurse anesthetist dependent on the surgical facility.
The decision on the type of anesthesia depends on the extent of face lift surgery, combined cosmetic surgery procedures along with the face lift, patient factors/preference, and surgeon factors/preference. Face lift surgery is a completely elective procedure, and safety is the most important concern. While cosmetic surgery may be performed for many individuals in an office setting, it's safer in your situation to have surgery in a hospital setting.
Only after a comprehensive evaluation by a plastic surgeon can one choose the appropriate anesthesia type for plastic surgery. Best of luck.