She's 13. People that age can understand right and wrong, but they are also particularly naive, inexperienced, easily impressionable, vulnerable to pressure.
The story as written is that she felt pressured by her classmates, and reading between the lines by her father, who seems very much like he had an axe to grind. Many children will probably buckle under the pressure of one of the (usually) two adults that they have most been conditioned to trust, respect, obey; or under their peers with a child's social desire to be respected, liked, and admired. In particular here, I'm thinking about what her father might be like and what an adverse influence he may be.
All sorts of dodgy accusations on all manner of topics occur all the time, including from adults. There also exists the context that the teacher really did show those cartoons. So whilst she lied, the base incident of showing pictures Muslims may find offensive did occur, so it's not a fabrication from nothing, either. It is tragic because it ended up in a death, but hindsight can mislead us. This in no way makes what she did okay, but this sort of thing is rarely going to end in catastrophe. There could not have been a reasonable expectation of such a terrible end by this girl at the point she lied: I would guess she probably just thought the teacher would be told off and have to stop doing it, and she'd win approval from her classmates and father.
I think we need to remember that we all do things which, on rare events, go horribly wrong. For instance, you can see people in cars obviously texting or chatting on a mobile as they drive, it is incredibly common. Many of us here have probably done it - maybe even just one call in twenty when we think it's urgent, and we try to end it ASAP. We KNOW it is wrong, that it can distract us and we can kill someone as a result... and yet we still do it, because 99.999% it doesn't go horribly wrong. We do this is in a zillion other ways, where we choose something we know to be a bit wrong, but it's easy / convenient, or we think it will impress, or whatever else, and we accept it because we don't think they will go catastrophically wrong. We need to remember that sort of context when we judge the 0.001%. Because we have done the sorts of things they did too: they just got the hugely unlucky result we didn't. They are not necessarily any worse people than we are.