Reminds me of my anorexic friend oddly enough. She lies that she is so thin because she has a super-human metabolism and that she eats like a pig, while I KNOW and have seen her cut a quarter of a toast bread slice into smaller dices before eating half of it for dinner...
I know the situation might seem opposite, but I think the problem is the same. Heavy people saying they eat like birds and have a mean metabolism and overly thin people saying they eat like pigs and burn better, they both do not want to belong in the norm.
Your friend's problem is probably part of a serious eating disorder that affects her mental health and social life. I'd be gentle but honest with her. I'd talk to her somewhere private, in a very friendly and concerned manner, trying to show I'm on her side and ready to help, not trying to make her feel bad about lying.
(though that didn't help with my anorexic friend... yet at least
)