Alright, while it is an interesting twist, the scientist in me has to point out: John Tolkien didn't create pointy eared elves. He may have popularized them, but he didn't create them. (And I never saw any extremely pointed ears like this until Blizzard's Warcraft came out.
You can see depictions of pointy eared elves in older paintings, like The Quarrel of Oberon and Titania, Sir Joseph Noel 1849; or (arguably) the Eadwine Psalter, Scribe Eadwine 1155-1160.
... That being said, it's clear that Lefay has been to Earth in relatively modern times. So why does she look like all the other "elves," if she's not an elf? What are the other elves then?
Also, she says she's the weirdest thing around, and the MC somehow agrees with her, but I'd say toothless granny was way weirder.