How to fix my lopsided lips?

Providing a photo would be best, everyone has asymmetry to the face but if it really bothers you I would advise to search for a highly skilled and qualified injector to provide you with the result you wish for 

Everyone has some degree of facial asymmetry. Do a google search for facial symmetry and you will see some striking celebrity photos.Nonetheless, it is important to consider mandibular (jaw) position and dental (tooth) alignment when evaluating oral aesthetics for symmetry. As you seek treatment, make sure these two points are addressed. That said, the treatment for mandibular asymmetry can often involve jaw surgery, and for dental alignment, braces and retainers are required.Accordingly, there are some smaller "fixes" that could be employed without as much effort on your part:1. botox injection to the depressor anguli oris muscles. This would allow a slight lifting of the corners of your mouth and eliminate some of the resting frown.2. juvederm or restalyne (filler) injection to the left lower and right upper lips. This could allow for more symmetry to be achieved.These treatments do not last beyond 6 months, but could provide you with a starting point for treatment. If the filler satisfies your desires for symmetry, you could proceed with fat grafting, which would be permanent.