I don't personally have this problem but I saw that you didn't get a response and wanted to try and help.
I did notice something that may be of use to you. I have seen some makeup artists use a lip primer to help even out lip color and lighten it before applying lipstick. There is also this Indian girl who has a youtube channel that I watch and she has darker lips and applies some of her foundation on her lips to lighten and even out the color before applying her lipstick which helps the color show through better.
There are also nude color lipsticks out there so if you find one that matches your skin you could try one of these.
Some people just have naturally darker and more pigmented lips.