I need to fix my lip after a dog bite. Is it possible to fix missing lip edge? (photos)

Hi and welcome to our forum!
From your photo, it appears that your initial injury was quite significant. Initial treatment usually consists of debridement of non-viable tissues, thorough cleansing to reduce the possibility of infection, and putting the remaining viable pieces together as in a jigsaw puzzle. In many instances, some of the tissue does not survive. Often infection following a dog bite can be serious and as a result the surgeon tries to use as few sutures as possible to minimize the presence of foreign bodies in the wound.
Basically, the purpose of initial treatment is to achieve a sealed healthy non-infected wound. In many instances, the scar heals satisfactorily. In others, scar revision(s) may be required for cosmesis. 
I recommend reevaluation by your plastic surgeon as I feel that there further improvement can be obtained with performance of scar revision, including red lip advancement.
Best wishes...