While I agree that Vitamin A will not be on the top of the list for healing leaky gut. There are many other higher priority items on the list to heal leaky gut.
Nevertheless, I want to note this what Patrick Holford wrote on in his book New Optimum Nutrition Bible …
“Vitamin A is also crucial for the health of any mucosus membrane including the gut wall.”
That makes sense because Vitamin A is known to be good for the skin. And your gut lining is like your internal skin. Just like your skin, it is a barrier between the outside world and you.
A good source of food vitamin A is liver. Or you can supplement with cod liver oil or other supplement forms. But be careful. Vitamin A can be toxic in high doses. It is not likely to overdose if you are eating a reasonable size portion of liver. But it is possible to overdose with supplements.
A safer way is to take beta carotene, which is water soluable and can be more easily eliminated by the body. Then your body will be able to make its own amount of vitamin A from beta carotene as needed.