So in that case, you have Sue being lied to. Her brother is not the subject, and Sue has the act of lying done to her. Is that not how you saw it?
I don’t think your translation is “wrong”. Sentences can be passive or not depending on how you frame them.
In your sentence it’s more like the brother is lying in general, but I do think the book’s version with it more directly implying he lies to her is the feeling the English sentence is going for.