I think doing a full lift under local would be highly unpleasant for both you and your surgeon. I would definitely not choose this option.
I have performed this technique under local anaesthetic and sedation on a couple of occasions for patients who were unable to have general anaesthesia. In both scenarios it was a very modest lift. I found that even with anaesthetic blocks that I needed to infiltrate quite a lot of anaesthetic solution locally. I felt this distorted the tissues and made it more difficult to perform the technique.I personally would recommend a general anaesthetic for this procedure unless there is a medical reason that you need to avoid general anaesthetic.