Would a lower facelift minimize the appearance of saggy fat deposits at the sides of my mouth? (photos)

For as long as I can remember I have had large saggy fat deposits at the side of mouth that really ruin my facial contours. These fat deposits (I assume) sit just on the outer side of where I anticipate my marionette lines will eventually be. I have no idea what to try to get rid of them but they really age me. Would a lower face lift or perhaps aqualyx fix them?