Would a lip lift make me look less ape-like? (photo)

Facial Xrays including a panorex X-ray, a full exam and consultation would be require to offer you the best opinion and suspect that a lip lift by itself may not be the best solution for you based on your limited photo provided.

Your apparent protruding upper lip may be caused by retracted premaxilla ( mid upper gum area) or protruded upper front teeth. Low nasal tip profile appear to accentuate the problem. Pre-maxilla augmentation  together with  Augmentation Rhinoplasty should significantly improve the problem while  Upper Lip lift may actually worsen it.