In my opinion, tattoos are meant to be seen by you and a select few others whom you trust. I’ve kept all of mine hidden for that fact, plus I know how hard it would be to get a job with visible tattoos. While all of my tattoos are hidden as long as I have clothes on, the one area that can be tattooed and will always stay hidden is a lip tattoo.
Lip tattoos are tattooed on the inside of either your upper or lower inner lip. Unlike typical tattoos, lip tattoos must be done in consideration of the veins in your lip. This makes it even more important that you get your tattoo done by a reputable artist. Another problem with lip tattoos is that they fade. This occurs because of all of the bacteria, acid and chemicals in your mouth, the ink is absorbed into the body much easier in that spot and that there is very high moisture content. Also, unlike typical tattoos, after a lip tattoo is finished the taste in your mouth is a mix of blood and ink. Not something appetizing at all!
For the aftercare, as with any tattoo, you need to consult your artist. They know best. Most recommendations are, of course, keep the newly tattooed area as dry as possible and to NOT use any alcohol or mouth wash with alcohol in it. Also, placing a paper towel between your new tattoo and your teeth can keep the moisture down and possibly help prevent fading.
Sources: http://www.ehow.com/how_4601995_care-inner-lip-tattoo.html, http://www.buzzle.com/articles/lip-tattoos-how-long-do-they-last.html
image credit: http://www.ibeatyou.com/blog/2010/06/08/craziest-lip-tattoos/