Who stands against the wall?

Is Lily leaning against the wall?

If so, she simply moved over to also let Peter lean against the wall so he could stand beside her.

That sentence does not necessarily state that Lily exchanged places with Peter. In fact, as i read it, she moved so that Peter could join her standing against the wall. So, Lily is standing against the wall. She shifts (moves) so that Peter can join her in standing against the wall.

There is nothing in that text to suggest that Lily changes places with Peter. She merely "moves over" (moves to one side) to make room for him.