A facelift, a mini neck lift or lower facelift can all be done under either local or twilight anesthesia (also known as conscious sedation or monitored sedation).  In fact, this is a preferable way to do these procedures.  Conscious sedation or straight local anesthesia has been shown to reduce complications like post operative bleeding, infections and DVT’s.  It helps to speed recovery as well.  This is because after the surgery you have almost no pain.  As a result, no narcotics are needed at all.  In fact, I have not had to prescribe an opiate for a facelift patient for 4 years.   For facelifts or neck lifts, all that is required for post op pain control in facelift or necklift patients who have had local only or local plus sedation anesthesia is an anti-inflammatory like Aleve (naproxen) or Aspirin.
Here is  a video of a patient who had a face lift with conscious sedation.