You should check your lipstick maybe it contains chemicals that make it darker. It's best to wear a sunscreen or sunblock on your lips to prevent darkening.

That is what I do, I use a lightener, sunblock and then apply lipstick.

I would suggest you buy some lip balm that has sunscreen and apply it throughout the day. A night put vaseline on your lips then scrub off the skin using a tooth brush. This works.

Use pink nipple cream to lighten the lips and while you are doing this make sure to use sunblock.