Can Surgery Repair my Lip? Had a Skin Graft After Mohs

Based on your description it sounds like excision of some of the skin graft with advancement of the red part of the lip would give you a nice result. You would need to share photos to know for sure. I don't use skin grafts on any part of the lip for the exact reasons that you note. There is not a great color or texture match with the lip. Seek a board certified Facial Plastic Surgeon or Plastic Surgeon to determine what options are best suited to your specific concerns. However, based on your description this can likely be improved.
Thank you for your question.Stephen Weber MD, FACS

I have never heard of needing to do a skin graft after lip skin cancer excision. I usually repair these with lip flaps or local flaps. Please call the office and schedule an appointment for evaluation.

Once Mohs surgical excision is performed most Mohs surgeons then place a skin graft as a temporary fix to get the wound healed and a consultation can be obtained from a Plastic Surgeon. This should be uniformly true for cancers in delicate and complex areas of the face such a the nose or lips. Cosmetic reconstruction of the lip is complicated and usually involves complete removal fo the skin graft and transposition of available adjacent cheek tissue to replace the entire quadrant of the lip while trying to match the opposite normal side of the lip. There have been textbooks written on the subject but  very few non-Plastic Surgeons are exprerienced in these operations.