I think devonapple has the right idea. There's a good reason the rule books have references to libraries and time to do research.
I think there should be two levels of difficulty for lore checks. The lower level is to know "Oh, yeah, I think I've heard of that, doesn't it have some weakness?" and the higher level is "Oh, that's an X! It's weakness is Y!".
Also, if your player is spending fate points on his lore rolls to get them super high, then he's obviously investing in knowing a lot. Let him have his fun with that. Skill points and fate points invested in lore checks means he's not putting those resources into other areas, so you can find other ways to challenge him where he's weak.
Finally, you always have a few other options, such as splitting the party once in a while so the others don't have the benefit of his lore some of the time. Or you could find a way to give him a compel to NOT know the answer to something.
Oh, and remember the catch rules - some weakness *aren't* known to anyone who hasn't done research (resulting in a lower catch value). Make sure you know ahead of time how much common knowledge there is about a given monster.