As far as Christian "allegory", the most prominent aspects of the Potter story that are applicable (in Tolkien's sense of the word) to Christianity are to be found in later books. But it should be noted that many of the themes ascribed to Christianity from the books are in fact universal archetypes, found in many ancient Hero Myths. So the connection to Christianity is definitely there, but it's a lot looser than many Christians care for, hence some of the controversy

I haven't read the Le Vay Fragment, so I can't comment directly on that. But, Rowling and Lewis are both drawing from an existing pool of literary archetypes and British "children's" authors' traditions, so it's not surprising that there would be other similarities, as well as the obvious Rowling "shout-outs" to Lewis in her books.
GB
