The asymmetry of your lower lip can be improved. The treatment depends on which side of the lower lip you like better. If you like the right side than the left side can be made fuller. If you like the left side than the right side can be reduced. Perhaps a combination would be the ticket. In any event, you need to schedule a consultation to discuss your wishes, learn about your options and come up with a plan. Hope you get the improvement you wish for!
Thank you for your question and photo. I agree that the left lower lip could be enhanced with a filler such as Juvederm or Restalyne. This should create much better symmetry without an invasive procedure. If you like the appearance with the filler, but do not want to come in every year for a "touch up", fat grafting would be another choice.