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Dry lips can be dark in color.
The other possibility can be dermatitis.
In cold weather, low hemoglobin, lips can be bluish in color
Cyanosis or low oxygenated blood can be a factor but he does not have any other symptom.
Keep the lips moist as you are doing.
Vaseline can be used.
Give adequate fluid.
If the symptoms continue, take him to doctor for an evaluation.
I hope this information will be helpful.
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Wish his healthy life.