The two issues you mention, deep nasal-labial folds and visibility of upper teeth when lips are relaxed open, may result from dimensions and relationship of maxilla (mid-facial bone) to other facial components. If so, lip lift not recommended, except perhaps as partial correction if you decide against orthognathic procedure. Surgery to anteriorly displace and vertically lengthen your maxilla may be indicated, and produce for you dramatic improvement.
Consult with craniofacial or maxillofacial surgery specialist in your area for information and for evaluation.
Based on the two criteria you are looking to improve, you would not be a candidate for a lip lift. A sub nasal lip lift does not change the depth of the nasolabial folds nor improve upper tooth show to any significant degree if at all. A subnasal lip lift does one thing very well...decreases the vertical skin distance between the base of the nose and the upper lip. It is one treatment option for the long upper lip.