Inner lip tattoos are notoriously difficult to maintain. The cells inside your lip are different from the skin cells where normal tattooing is done, and don't hold the ink as well. In addition, saliva breaks down the ink just like it was food. If it isn't touched up, your tattoo will last between a day and a week. It normally requires 3-5 touch ups to become "permanent", although it will appear more faded than a normal black tattoo. With all of the work, and rework, the design tends to get blurred unless it is very simple. (Hopefully your tattoo artist let you in on all of these details.)
While on the subject of tattoos, I have "It takes strength to be gentle and kind" under my collarbone. I also have Joan of Arc burning at the stake on my right arm, but I only consider this to be Morrissey-inspired, and not a full-on Morrissey tattoo. I strongly resisted all urges (and half-joking suggestions) to include a hearing aid or walk man in the design.