Lip numbness is rare, but it's possible. Your wisdom teeth are close to the inferior alveolar nerve in the jaw. According to the NHS, if the nerve becomes damaged during the procedure, it can lead to numbness in the lips or jaw. This numbness is usually temporary, but it can be permanent if nerve damage is severe. Most wisdom teeth extractions do not have this complication, however.
Your dentist or surgeon will discuss with you possible wisdom teeth extraction complications and their recommendations for reducing risk, including taking care of your extraction site after the procedure to ensure proper healing. Follow their aftercare instructions and contact their office if you are concerned about a side effect or complication of your wisdom teeth removal.