Would Lip Wrinkles Affect Permanent Makeup Results?

I occasionally work with an aesthetician who performs micropigmentation. She has commented and actually prefers that a filler be placed prior to pigmentation because it makes her job easier to apply a smooth border to the lips. Discuss this with your professional.

As long as you find a good permanent makeup artist, the lip lines around your lips should not affect the permanent lip color.  Ask the provider if you can see some of their before and after pictures of older women who have had it done to get an idea of the quality of his/her work.

The problem with the vertical lines around the lips is that regular lipstick will bleed up into those lines. Permanent make-up will help solve that problem. There are a few things that can be done to improve those lines prior to the permanent make-up procedure which will make it easier for the tech.
Consider a CO2 laser resurfacing procedure around the mouth area. This will substantially smooth those lines. Tissue filler, like Restylane or Juvederm, will temporarily smooth the lines. The permanent make-up technician should have no problem implanting the pigment even without pre-smoothing the lines but the final result will be more pleasing if those lines are addressed.
I would also recommend you select a technician who works with a board certified dermatologist or plastic surgeon to ensure a safe experience and a quality result!