I assume this is from chemo, the various side effects, infection, angular chelitis, dehydration, lack of sufficient nutrition... I used vitamin A & D ointment in the hospital, vitamin E, I believe, and biotene dry mouth gel on my own, including fungal, anti-bacterial medications when given. Vaseline I heard not to put on the lips, but really forget why or if so, applying ice chips may to soothe the lips may help too, but check with the doctors, nurse as to the cause, treatment.
Good luck.