Okay, here goes some facts... (and it will depend on the type of lift surgery they are doing)... If you are having implants, they make a tiny incision, work the implant into position and inflate it. It is non-invasive, but you will be very sore and bruised. If you are having any reduction (removal of skin), then it is a more invasive surgery and you should definitely avoid food, alcohol, and Nicotine 12-hours before surgery, and you should avoid any stimulant, alcohol, etc. for several days after surgery.
Fact 1: (most) Doctors hate the idea of anyone smoking or vaping... so they want you to stop (period). Many doctors also have deals with Big Pharma and get kick-backs from prescribing medications such as Chantix, Nicotine inhalers, or patches (even though you can buy them OTC). So, if you are "self-medicating" with a vaporizer... you're taking money from their pockets!
Fact 2: Hospitals have deals with Big Pharma to provide you with Nicotine patches (whether you want them or not) at the price of about $100/patch... billed to your insurance company. This is the way hospitals "control" Nicotine inside their walls. If Nicotine were a bad thing, they wouldn't hand them out like candy to all patients who use Nicotine... yeah, think about that one for a while....
Fact 3: Nicotine is a stimulant which raises your heart-rate... not a good thing right before invasive surgery
Fact 4: Nicotine is a vasoconstrictor which increases blood pressure (slightly)... not a good thing right before invasive surgery
It won't kill you to go without Nicotine for a day or two... especially if you are having an invasive procedure, you won't even want food/water for a day or two. If you are having a standard "lift", you'll be home and doing your daily routine after a few hours, and you should be perfectly safe to continue vaping a few hours after surgery. It won't kill you, nor will it have any adverse affects to the implants, incision, etc.
As @Tam said, however, speak truthfully with your doctor before the procedure to know how it will affect you, and what you have to do to heal properly. But, take his advice on all the evils of vaping with a cautious and skeptical ear.