Is there a reason why she'd lie about going to the library? Do you let her go to the mall sometimes or are you a 'study parent', the kind of person who sees weekends and evenings as more study time rather than leisure time? I'm not having a go at you, but going to the mall seems like such a tame thing that I wonder why she'd felt that she may need to lie about it in the first place.
Unless of course it is the friend's parents who are the study parents and the friend may have assumed that you were the same.
But either way, I think that she needs to understand that going to places like the mall, the cinema, the bowling alley are not things worthy of having to lie about...............renting a chalet at Costa Sands with a bunch of teenagers of the opposite sex and partying the night away on the other hand is rather more worthy of lie

She needs to get her priorities right
