Vertical lip lines llocated above and below the lips, also called "lipstick bleeding lines" (because lipstick typically bleeds into them) or "smoker's line" (although many nonsmokers have them), is a common problem resulting from chronic overexposure to the sun, genetics and the passage of time.
At one time, not that long ago, this problem was difficult to treat. Medium (such as TCA) and deep chemical peels and ablative laser surgery were the only approaches and these procedures were frought with prolonged downtime (recovery time) and the risks of scarring, prolonged redness lasting months, and permanent loss of pigmentation.
Today, most cases can be improved quickly and easily, with little downtime and few potential risks. My favorite approach is to start with Botox or Dypsort instilled in literally microdroplet amounts to the upper and lower lip regions to diminish the movement-related contribution of the muscles (i.e. dynamic wrinkles) around the mouth. If necessary, to supplement this effect, prolong it, and to deal with wrinkles present at rest (i.e. static wrinkles), I very superficially inject iny amounts of a filler material (such as Juvederm or Restylane).
Other current treatments that I have found helpful for this problem and that also engender little in the way of downtime and risk include radiosurgical skin tightening, mesotherapy, and medical microneedling.