I have had 2 skin grafts- one on my body and one on my gums. The skin graft on body is hypopigmented/scarred, which does not tattoo. So, a tattoo would not take on scarred lip skin. And there is a tire patch (a patch of gum tissue that is a paler in color than surrounding gum tissue) where I had my gum graft. Overall, a skin graft is not a good idea. You do not want different colors on your lip.
I think doctors cut the EC area out so your lips become smaller. I am not sure how they replace the removed part if you do not want your lips smaller.