If you're considering a lip lift while undergoing orthodontic treatment, my advice is to complete your braces or teeth alignment first.
Your teeth are the foundation of your lips, significantly impacting their appearance. For instance, boxers wearing mouthguards seem to have fuller lips, but it's the guard pushing them out, not filler.
Conversely, someone with no teeth has little lip support. Proper teeth alignment can drastically affect your lip lift results, so finish orthodontics before surgery for the best outcome.