Yes and no. The inner lip is a very weird spot to tattoo and a lot of artists won't even do it unless it's on friends. They could theoretically hang their needles out a small amount and not push and hope it only goes in a few layers BUT everyones body reacts different to being tattooed. A lot of lips do fade/fall out and it's usually from artists not going too deep the first time because they don't want to blow the tattoo out.