While you work on correcting the underlying issue of chronic lip problems, you can soothe your lips and speed up the healing process with the topical application of vulnerary plants - these are herbs that have a healing action on damaged tissue. Two of the best for cracked and split lips are Calendula (Calendula officinalis) and St John's Wort (Hypericum perforatum).
St. John's Wort flowerheads have proven skin protecting and regenerating properties, and help to repair epithelial damage of skin. Calendula flowers have wound healing, anti-inflammatory, antiseptic and skin restoring properties. Healing creams and balms made with plant oils and plant extracts are naturally protective and allow the skin to breathe and regenerate unlike mineral oil derivatives such as petroleum or paraffin in conventional creams which may dry up the lips even further. Apply the natural cream or balm to the lips, three to four times daily, until your lips are healed.
I hope this response has provided some further insight for you. If this condition worsens or does not improve, please see your leading healthcare professional.
Reference:
Referen Lavagna, S. M., Secci, D., Chimenti, P., Bonsignore, L., Ottaviani, A., & Bizzarri, B. (2001). Efficacy of Hypericum and Calendula oils in the epithelial reconstruction of surgical wounds in childbirth with caesarean section. Farmaco, 56(5-7), 451-453.