How many clues do you need that it is related to what you eat or how you eat ?
Would you like your lips to write a message to you:
"Dear lip owner, the reason why I, your bottom lip, get red after you eat is because you eat !!!"
People can actually be allergic to many things. It works like fire.
Lets say you are allergic to gluten (it is called gluten intolerance).
But, you ignore that intolerance for a long time.
Due to the specific effect of gluten intolerance, your body and your intestines may actually become sensitized to many other foods that you consume together with gluten, making it appear as if you are also allergic to all those other foods like milk, night shades, berries, sugar, fruits, eggs, shrimps, fish, soy, corn, rice etc.
But, once you eliminate gluten, your body and your intestines stop being irritated by a strong allergen, and suddenly all those those other foods (or most of those other foods) may stop being the trigger of your red lips.
Now, this may not happen exactly suddenly.
It may take some weeks or even months on gluten free and milk free diet, especially if you have been gluten intolerant for a very very long time.
Healing time is proportional to the time you were intolerant.
If I were you, I would forget all those blood tests which, buy the way are sometimes useless, and I would try to live for 2-3 weeks 100% gluten free, 100% grains free, 100% Sugar free (sugar added to food) and 100% milk free.
If you are sensitive to gluten or wheat or milk or Sugar (these are the most common sensitivities), and if those foods are the trigger of your inflamed lips (red = inflammation = allergic reaction to specific proteins and specific sugars and maybe other molecules found in specific foods )
That simple experiment may answer your question.
What can you eat ?
Research the paleo diet, or the keto diet, or the vegan diet, or make your own diet free from those common trigger foods.