When I talk, my lower lip bends to the left. It also happens when I smile.

This is tough to answer without pictures. A combination of fillers (juvederm, restylane, volbella) with botox and lasers can help define the lips. I recommend getting a formal evaluation with a cosmetic dermatologist. Best, Dr. Emer 

Thank you for your question. It is difficult to give you advice without seeing a photograph or evaluating you in person. Based on your description you may benefit from the use of Botox or dermal fillers.Dermal fillers such as Juvederm is good option as it is a hyaluronic acid fillers that can easily be dissolved with an enzyme known as hyaluronidase, if you are unhappy with the results. I recommend you consult with an experienced injector to determine the best treatment plan for you. All the best!

It might be possible to treat the mouth area with Botox/Dysport and fillers to improve this problem. I can't really say exactly what I would do without pictures and full motion videos. The new fillers, Restylane Refyne and Defyne are made to move naturally with expression and might be the ones used in a case like yours.

Thank you for your question.  It is difficult to comment without seeing a photograph or, ideally, an examination.  Based on your narrative, Botox and/or filler might be good treatment options for you.  Please be sure to see an expert injector for an in-person consultation to fully discuss your goals and expectations in order to determine the best treatment plan.  Hope this helps and best wishes!