I personally think that it's the mother who should be challenged. It is her responsibility as a parent to teach her child that lying is evil and has consequences. It is a violation of personal honor, the child needs to learn this.
I think that as a result of these incidences that the GS Council ought to consider placing the girl in a troop of third graders where she would be better able to cope socially. Just because she is in the 5th grade in school does not mean she automatically should be allowed into a 5th grade GS troop.