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A dry, white and scaly area around the lip appears as a result of the allergic reaction to the saliva. It is medically referred to as dermatitis, specifically called cheilitis, when it is confined to the lips and the area around it. This could be due to other allergens sometimes, food items like strawberries or other berries might cause them, but it is very common among individuals who have the habit of wetting the lips with saliva. Using coconut oil on the lips will not help with the dryness. Still, if coconut oil is applied on damp lips and areas around the lips, it can help since the immiscible combination of oil with water forms a creamy consistency which will help with the dryness. You need to make sure to leave the oil on the lips only for one hour before washing it off. Instead of using coconut oil, I suggest applying Evion 400 (Vitamin E capsule). Break open one capsule, mix the content with aloe vera gel, and apply to the lips. Leave for two hours and wash it off. Repeat the same daily for one month. It helps with discoloration (darkness) and dryness. I would also advise Moisturizing creams like Sebamed lip defense with SPF 20 lip balm or Neutrogena lip balm with SPF 15 (whichever is available) to be used on the lips in the morning and night. It can be used even while traveling and going out and before going to bed at night. Take Capsule Becosules Z (combination capsule of vitamin B complex, zinc and vitamin C) once daily at night after food for two months. Use Light scrubbing lips once in two weeks can help eliminate the dryness. Very gentle scrubbing with any lip scrub available commercially can be used. Drink at least 10 to 12 glasses of water through out the day. Dehydration can make your lips drier. Avoid licking of lips, having unusual berries or any allergens that might be leading to dermatitis. I hope this can help.