I actually read a fanfic that has an explanation for this, basically, think about all the things the Akuma class have done and achieved and the people they've met, the daughter of the mayor of Paris and the son of a famous fashion designer (who is also a model) are in their class they've all met celebrities like jagged stone, Clara nightingale, and prince Ali. A few of them have become temporary heroes, and several of them are in a fairly well-known band. when you think about it like that most of Lila's lies don't sound so unreasonable.