Hello and thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 25 years experience and would be happy work with you.
What it sounds as if you are describing is a condition known as feline eosinophilic granuloma complex. This is a condition in cats that has allergic reactions as it basic problem and the lesions can present in different ways. Sometimes it is just the "pouty lip" or swollen lower lip and other times it may be in other ways including upper lip ulcers or plaques on the body.
In many cases, they don't bother the cat at all, and will resolve in a few days with no treatment at all. In more severe cases, they may require a short course of steroids, but if they become a recurrent problem, especially if needing steroid frequently, the cause of the allergy should be investigated.
Here is a link with more information about this condition in cats. LINK HERE
My own personal cat is affected by this and had had two episodes of the swollen lip and one episode of pretty severe ulcers that required steroids. He is currently on a food trial to rule out food allergies. Here is a better picture of the swollen lip that is portrayed in the link.
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.