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.
One condition that can sometimes be misinterpreted as dry skin on the lips but is actually quite different is something called angular cheilitis. This is a condition in which the skin at the corners of the mouth where the lips come together is reddened, peeling, and cracking. This condition is not caused by excessive dryness or chapping; rather, it is sometimes a fungal infection of the skin (which can easily be treated with anti fungal creams or ointments) and sometimes it is related to a vitamin deficiency.
If the condition persists despite good lip moisturizing and avoiding picking at the skin, or if you think you might have angular cheilitis, then I would recommend that you get in to see your primary care doctor
to determine whether or not additional treatment is needed.