Lips peeling is a common condition. There are many causes, some of which require minimal treatment and some of which are require medical attention. I would suggest you see your primary care doctor
to have this evaluated.
In general, your lips are a unique structure. They are structures that are supposed to be moist like the inside of the mouth, however are located on the outside. Therefore one of the most common problems of the lips is drying out of them. Dry lips, or chapped lips, can subsequently result in blistering and fluid discharge. This requires only hydrating solutions, like petroleum jelly. A more severe form of chapped lips is known angular cheilitis or stomatitis. This can be caused by many causes-- including nutritional deficiencies or autoimmune diseases. Either of these two conditions can subsequently be infected with either bacteria or fungus and have further discharge. This requires treatment.
Another condition to consider is if this is a primary infection. Herpes actually presents similar to this. This can be treated if your doctor diagnoses this to be the cause.
What is occurring on your lips can be from many different causes. Your doctor can diagnose what is causing it. Treatment depends on the cause. Good luck!