Honestly telling there is no cream or medicine as such which can cure the dark pigmentation of the lips. You should apply a good lip balm with sun protection factor (spf) whenever you go out in the sun. Other than that keep them well moisturize by keeping yourself adequately hydrated and consult a cosmetologist as Nd YAG laser has been found to give promising results in hyperpigmented lips.
I hope it helps. Take care and please do keep me posted on how you are doing. Kind regards.