Will a Lip Lift Correct a Low Smile Line?

I have a low smile lip-line, I know its genetic my father has the same thing. My top teeth don't show when I smile, only about 1mm of my top teeth show when I'm laughing. I'm wondering if a lip lift will correct this? I want to have a big toothy smile :D I don't have an underbite or an over bite. I do have a small mouth and thin lips which probably doesn't help too much with showing teeth when I smile. I'd just love to have teeth show when I talk and smile. Hoping to get some good news here.