What's the best treatment for a Venous Lake? (photo)

I have been my whole life with a blue-purple vein on the right lower part of my lip and i want to get rid of it, my currently demartologist has been treating me with the Pulsed Dye Laser for the last three months(one session each month). The problem is that i'm not seeing any big improvement and i'm getting a little worried because i really want to erase this mark off me, i have been struggling my whole life trying to hide that imperfection and avoiding talking to people or showing my face.