Facelift Disproportionately Fat Face?

Fullness in your lower cheeks is a very common trait that is quite difficult to correct completely, however improvement can be made surgically. Without seeing your photos, I'll answer the question in general terms. You are very young to have a facelift, but assuming this is what you're interested in exploring I'm going to address to the question of what surgical option is most likely to be effective.
There are few surgeon's that resect Bichat's fat pad during a facelift since it is in a territory referred to as tiger country because of the high conentration of facial nerve branches. You should find the ABPS BOARD CERTIFIED PLASTIC SURGEON in your area that is comfortable with this and has photos to share his experience with you.
Yes, once the fat pad is decompressed/reduced there will be sagging cheek tissues. These will need to be lifted and resuspended thus requiring a facelift.
Some resect this tissue with a tiny suction cannula but I think that's not a safe way of doing it since there are so many facial nerves there that control the movement in the corner of your mouth, suctioning is a blind technique and not my favorite way of doing it for that reason.
Lastly, I would warn you against your initial hunch of just tugging the skin laterally showing a significant improvement. There's plenty of people out there that would do that for a small fee. The tension will be there with a facelift but it will not fully correct the problem in the long term.
Eventually, the tissues from the pull will relax, the facelift scar will widen (over the years), and the cheek will bulge back through an unnatural "lateral sweep," where the wrinkles on your cheek sweep in the shape of a nike swoosh! It is potentially a pretty unnatual look. If you only lift up on your jawline and don't lift up your cheek, how will it look later on when your cheek continues to descend and your jawline didn't? My intent isn't to pose more problems, it is simply to reinforce the fact that your anatomy requires the skill of an ABPS Board Certified Plastic Surgeon that does Aesthetic Surgery.
The marionette lines can be improved with fillers, not a biggie. The turned down corners of your mouth is a little trickier but I've seen great great results just by using fillers causing some really nice optical illusions that show drastic improvements.

You sound too young for a facelift. Perhaps liposuction of your cheeks and jowls are sufficient at this time, however, I would not rule out the lipo combined with the facelift entirely.

The majority of patients seeking Facelift are age 50 and older.  A person in their 30's is generally not a candidate for a variety of reasons, but most importantly because the aging changes that can be addressed by Facelift are not present.  Secondly, Facelift is not usually considered a "facial slimming" procedure.  What would be most valuable to you would be a consultation with a Board Certified facial Plastic Surgeon or Plastic surgeon in your area.  There are some noninvasive treatment modalities, like Botox, which can reduce the size of your parotid gland and masseter muscles on a temporary basis.

It is usually not appropriate to do a facelift procedure on a thirty-three year old patient. If the problem is truly a disproportionate fat face, liposuction could be considered an option in the neck area however, I highly discourage liposuction to the face. Facial fat is very important and it is lost naturally as we age. Therefore, I do not recommend liposuction or removal of fat to the face and I do not recommend a facelift for the reason of facial fat only.  

It is difficult to asses you without pictures but most likely you would not be a candidate for a facelift.  First of all, patients who complain of excess "fat" in face or neck or any other portion of body should use diet and exercise as means of addressing.  In some cases, neck and facial fat is resistant to changes here despite making an admirable effort in slimming down.  Facial liposuction is typically a bad idea in a face because it can leave subtle irregularities in the skin contour, while neck liposuction is safe to perform.  

All faces are different and in your case analysis with a surgeon may help achieve a better balance and proportion to your face and could include buccal fat removal, botox facial reshaping, use of facial fillers to just simply recommending a good diet and exercise plan.

Your face is composed of skin, fat, muscle and bone. Disproportion in any of these may result in a face that may lack harmony. You may benefit from enhancing the jawline with chin implants and or liposuction in addition to the facelift. 

Jowls are those pesky fat pads that migrate from the cheeks into the jawline. They are being pulled by gravity across the jawline and create the marionette lines trailing from the corners of the mouth that enhance the perception of "frowning". The maneuver to make this look better by pulling on the skin toward the earlobes is what leads patients to consider facelifting. There are disappointments in those with excesive weight in the cheek tissue because of the inability to relieve the jawline of the mass effect. If the weight is not effectively removed through liposculpture, weight loss, or surgery, you may expect an early recurrence of the aging face and the frowning marionette lines.

The beauty of aesthetic surgery today is our ability to address concerns with a tremendous number of options which were not available just a few years ago. Our understanding of facial aging and how to approach it has also become more refined.
I like the others, who have answered your question, can't give you the answer you need without evaluating you but a few things come to mind when reading your question.
Your concerns about the downturned corners of the mouth can be addressed by injecting botox into the muscles which pull down the corners of your mouth. The marionette lines can be improved with facial fillers to soften the transition.
Without seeing you my instincts are you are not a facelift candidate because of your age but a consultation woudl clarify that issue. At most a buccal fat removal could help by decreasing the mid cheek volume and creating a more defined face.
Seek out an experienced plastic surgeon to help with this decision.
Good luck.

 It is not possible to say for sure without examining  your face. Sometimes you can get away with liposuction only. But it sounds like you need both a liposuction and a minilift to tighten the sagging skin.

Although anything is possible, a true Facelift is something that is rarely needed for someone your age. Having said that, I preformed a "re-do" on a woman that was in her mid 30's! The problem for her was that she received a SMAS lift and without having the dissection expend to the corners of the nose and mouth, the pull on the skin did not provide her a lasting result. One year after her SMAS Facelift, I performed a laser vertical Facelift.
One option to consider are skin fillers. Some are more lasting than others but that can help fill out the lines you described. It depends on how prominent the lines / sagging is.
For the fullness of the cheeks, you can have the buccal fat reduced. However, this can come back to haunt you years latter as a fullness of the cheeks can be considered "youthful."
The best thing to do is seek consultation with a few certified Plastic Surgeons that understand what I have discussed.
Hope this helps.