Chewing gum may be a pleasurable experience for some, but it is neither good nor advisable for healing facelift patients. As the skin flaps heal, gum chewing can cause a couple of (serious) problems.
One, repeated contracture of the facial (jaw) muscles could cause bleeding in incompletely-healed blood vessels, causing lumps and irregularities (minor bleeding) in your face, or hematoma requiring re-operation to evacuate the clots beneath the facial skin.
Two, gum may stimulate significant parotid gland saliva production, and if the gland was irritated or slightly injured in the facelift skin flap elevation, saliva could collect beneath the skin flap rather than draining into the mouth as it normally does. Salivary cysts can cause healing problems, infection, and may require re-operation.
If you really believe that you can "exercise" a double chin away with ANY kind of facial exercise, I could probably interest you in a Mark Eden bust developer! (This was a plastic spring-loaded device from the 1970's that a woman could use to "exercise" her chest muscles for breast enlargement--it worked as well as the estrogen bust creams and the breast-growth pills sold today!)
Also, you should not chew gum on the morning before surgery. Even though you are not "eating or drinking" as advised, chewing gum stimulates stomach acid production and increases the risk of lung injury from aspiration pneumonitis.
Just say "NO" to gum! At least if you're having surgery. And for at least a couple of weeks after facelift. Best wishes!