A marionette is a puppet controlled from above using wires or strings. These puppets moved their mouths by moving their lower lips and chins as a single unit. In live human beings, marionette lines refers to those paired lines that go from the corners of our mouths then down and out to each side of our chins (like a puppet). There are 3 reasons that marionette lines form.1. Solar aging of our skin from sun damage and time passing.2. Deflation or atrophy of fatty tissues in our faces as we age (even obese people get deflated faces).3. Ptosis or falling of the soft tissues on our faces.Fixing them requires:1. Skin care, skin resurfacing with lasers or chemical peels2. Fat grafting or transfer to replace and replenish the deflated fat compartments of our faces.3. Lifting of the soft tissues back up to where they are supposed to be with a facelift.Liposuction will NOT fix marionette lines. In fact the OPPOSITE (fat transfer) is the treatment. Liposuction may make your neck look better by removal of submental fat, but will not address your marionette lines.Looking at your picture, you probably don't need a facelift yet. I would recommend Botox injections into your DAO (depressor anguli oris muscle) - 5 units on each side. This will help prevent the corners of your mouth from pulling down by temporarily weakening the muscle that pulls them down. I would also inject filler or fat into your marionette lines to "fill the wrinkle/valley." All of this could be done in the office under local anesthesia. Filler being temporary, fat transfer being more permanent.