My lips don't close naturally and it looks really awkward. What can I do to correct this? (photo)

Thank you for your question.  I agree with my colleagues bellow.  You should see your dentist first.   Many injectors will attempt Botox, fillers, but it is best to address the underlying cause.  

Thank you for sharing your question. I would advise you speak to your dentist, and possibly and oral maxillofacial surgeon to discuss your skeletal anatomy as a reason for your lip closure difficulties.  Hope this helps.

I would first see a dentist. It could be an occlusion problem related to teeth or the jaw. Also chronic mouth breathers need to keep their mouth open. If all evaluations are negative, filling the lips with HA filler will get them closer to touching.