After my lip tattoo a week ago, I noticed that it's getting darker. (Photo)

As the lips heal, the color gets lighter, and then as the skin heals, the color typically darkens again in pigment. Two weeks after the initial procedure is when you usually see the truest color.

Hi there,
I am a certified permanent makeup technician and have come across this type of concern. First, one the Fitzpatrick scale of 5/6 are rarely performed on for lip procedures. Resin being color retention, melanin production or worst case if a improperly trained technician goes to deep you could end up with vitiligo. This case seems to look like you may have a production of melanin darkening the lips or possible sight bruising which could occur. 
As a certified technician I would recommend that you fully heal. Then, if it is still prominent there are ways to improve the coloring. Your trained technician should be able to lead you in that direction. I personally like to have my clients who has hyperpigmentation this use Skin Medica  Lytera 2.0 that is a tyrosinase inhibitor. Along with always protecting with SPF 50.
Note: Depending on where you stand on the Fitz Scale determines the pigment coloring. Example- Fitzpatrick 5/6 will never have red lips they will exert dark maroon. So please, follow up with your trained and certified technician. 

 Hope this helps!