Hello and welcome to health care magic forums.
Usually the skin around stitches will take 7 to 10 days to heal properly and the healing will be complete by 1 month, depending upon the site of
injury, depth of the cut and infections if any.
Usually the doctor will give antibiotics for 5 days to accelerate healing and prevent infections.
The black colour will gradually fade and will disappear when healing is complete. It's not permanent.
But the stitch marks will persist for a long time. You haven't mentioned the exact site of the wound on your lower lips. If it involves the inner side of mouth, it's better to avoid brushing for a week. Instead apply tooth paste in your index finger and brush gently without causing much disturbance to the wound. You can use a good mouth wash twice a day to improve
oral hygiene.
About dressing of the wound, it's recommended to go back to the hospital where the stitching is done, every alternative day, so that nurses will do the cleaning using
Povidone Iodine.
Hope this discussion will be helpful to you. Have a great day