Thanks for the query.
Drinking enough water solves many issues and in particular cannot be related to darkening of lips. Is there any other medical condition you are suffering from? I suggest you to meet a qualified Dermatologist who can physically examine you and reach a diagnosis.
There are several products available to help you with the condition. Till then apply a lip.balm with sun block to prevent further darkening of lips.
Hope it helps.
Dr MK Agarwala