What is the Best Non Surgical Treatment for Lines Under Eyes and Around Mouth To Give a General Lift and Improve Skin Surface?

That is a difficult question to answer without seeing photos or being able to evaluate you in person. Some things that can be helpful are chemical peeling and/or laser treatments (resurfacing and tightening). When done correctly, injectable neurotoxins (ie. Botox) can also sometimes give lift around the mouth. I recommend you consult with a board-certified dermatologist or facial plastic surgeon.