I don't think this is a good idea. Your face's blood supply after a facelift is somewhat compromised for a while, until it "learns" how to get blood and drain it, and I would not want any medications (natural or otherwise) on it until several weeks have passed. That, however, is my opinion, and not your surgeon's. You should check with your surgeon for their advice. Good luck!
You should definitely speak to your physician regarding this. Although Aloe Vera has been used for decades for sunburns or minor cuts and scrapes, it could cause irritation to the skin of the face after a Facelift. Seek your surgeon's opinion on this, as it may a patient to patient basis.