I believe that being on anticoagulation is a direct contraindication for facelift/necklift surgery. The biggest problem that could happen is significant bleeding (hematoma) that could cause airway compression, skin necrosis, significant blood loss requiring fluids/transfusion/iron supplementation, and even possibly death. There are some select patients that can be operated on with the help of a hematologist/oncologist to ensure that the blood thinner can be held for surgery and properly resumed when deemed an adequate time frame (by both the plastic surgeon and heme/onc MD). In general, I would recommend avoiding any unnecessary risk, but as long as everyone is aware of the potential risks/complications/complications, it is a possibility.