There is a Summer / Autumn / Winter / Spring pattern in the Temperate zone, also affecting the Desert and the Grassland climatic zones and, a Wet / Dry pattern in the tropical north which includes the Equatorial, Tropical and sub-tropical zones.
Most likely, your lips are suffering from excessive dryness, or chapping. Actually, picking at them and peeling off the skin can worsen the situation, as this can make the dryness worse. It would be better to try applying a good lip balm or lip moisturizing lotion. This should help you break the cycle of dryness and peeling, but only if you can refrain from picking at the skin in the meantime.
3. Cold Sore. Itâs also possible that the dry patch on your lip is a cold sore or at least the initial signs of one. A cold sore tends to be accompanied by more than just a dry patch, however. The affected area will likely itch, burn, and/or tingle for a day or two before a series of blister spots appear.