I wish there was one "slam/dunk" treatment for vertical upper lip lines.  They can be 80-90% corrected but it takes a little time, money and patience.  There really is no one treatment that works perfectly so we combine things.

In my opinion, if the lines are just starting or are minimal, a few tiny drops of Botox coupled with a light laser like the Fraxel or a fractionated CO2 like the DEKA dot works well.  The lasers cannot be used just on the upper lip if you are tan or sun damaged because you'll end up whiter on the upper lip.  Not a good look!  Then, you have to do the whole face to blend it which may be a good option anyway, if you have sun damage. 

If the lines are deeper, then a filler like Juvederm or Restylane in the lines is needed to fill in before the laser.  The same information regarding the laser applies. A few drops of Botox are still nice to help prevent the lines from recurring and make the Juvederm/Restylane last a little longer.   Dr. I