"Doesn't it mean that the cause can't be internal? Because otherwise all of the lip would be affected, not only certain parts of it."
How did you get this conclusion ?
If some different parts of your lips correspond to a different parts of the digestive tract, there is absolutely no problem in having just some parts of your lips affected by EC, and not all of your lips.
If just some parts of your digestive tract are inflamed, or irritated, or weak, or inhabited by subperfect microbiome, or inhabited by some harmful bacteria or fungi or have been damaged by Antibiotics or by some other medications like accutane or artificial hormones ... and if health of human lips is often just a picture of health and everything/anything going on inside your intestines, then ... there is no problem in having just some parts of your lips affected by premature skin death, while the other parts of your lips continue living healthy life, no premature skin death.
EC is nothing more but premature skin death, very similar to Seborrheic Dermatitis (common on other face parts), dandruff (common on scalp), and some other forms of dermatitis like pompholyx (common on fingers) ....
Most forms of eczema result in premature skin death on some part of your skin.
"Evolution created" humans in a way that they very often advertise their internal health on their external body, like face, teeth, hair, nails, skin, body shape, voice, eyes, lips etc..
That way, a potential sexual partner has a chance of making an important choice.
If there is a possibility to choose between having sex (and that usually meant having kids ) with someone who has a perfect skin and having sex with someone who has possibly imperfect skin, statistically, a choice will be made more often of having sex with a person who has perfect skin.
When that happens over 1 000 or 1 000 000 generations to over millions of people .... it becomes an important evolutionary advantage ....
So, if you are to have kids with someone who has perfect skin, or with someone who has imperfect skin ..... you kids have actually much better chances of being healthy and that on the evolutionary scale often means much better chances of survival if you choose a partner with a perfect skin.
After 1 000 000 of generations .... "evolution has seen" that there is a great advantage if humans can advertise their internal health and their age on their skin and face ... as on the long run it gives much better chances of survival of the species as whole ...
Several times in the human history, humans have been close to extinction, last time 70 000 years ago.
That is why we, humans, as species ... advertise our health and our age on our face and on ours skin, eyes, hair, voice, skin smell etc. ...
So, if you still have any doubts that whatever happens on your skin has nothing to do with your internal organs .... think again .... before it is too late for you ... before you become extinct!
Evolution is very cruel to those who are born blind!
P.S. Vi are not unique .... dogs and cats (and most other mammals ) advertise their internal health with health of their fur, and their smell, birds with their feathers, fish with ...etc...