I’m an American and have never heard the expression “food lion” or any similar use of “lion,” but Elen’s guess seems pretty reasonable. Americans do use “lion” like this: “He was a lion of the legal profession” — meaning he was a leading and courageous lawyer.

Food Lion is the name of a chain of US supermarkets, popular in the southeast United States. I don't know if that is part of the answer. If Brian was lying about food... for example, if he was trying to lose weight but secretly eating candy bars... I can imagine a pun on "food lyin'" and "Food Lion." That's just a wild idea.

It’s not an American expression and I have no idea what it means. And I’m a US native speaker.

you eat a lot of food brian I think