Can I get liposuction around the nasolabial folds? (Photo)

The very very short answer is NO!The nasolabial fold is from excess skin hanging over in a drapery effect.  If you suck out what little fat there is and break up the fibrous tissue, you will get even more drapery effect, i.e. this is a very bad idea.Secondly, a SMAS lift is part of a lateral facelift which has very little, if any, effect on the overhang of the nasolabial fold.  A mid-face lift, which is an elevation of the tissue from the inner canthus of the eye to the corner of the mouth and back to the outer canthus of the eye, can cause a great improvement in the depth and appearance of the nasolabial fold by significantly decreasing the drapery effect.At this point, I highly recommend you find a Board Certified plastic surgeon in your area who has extensive experience in mid-facelifts.  

Seems you have a slight asymmetry in the muscular function, preop and postop better views would help to understand your problem.For sure, liposucion at ANY area of the face is an absolute NO-GO, reckless. Real danger of irreversible functional and aesthetic damage.Seek better opinions.

Thank you writing to RealSelf and submitting a photo. Liposuction of the areas just lateral to the NL crease will bring about some improvement.