It means "my parents gave me a nontraditional name because they thought it would be cool".
I don't think it "means" anything. Jay itself doesn't mean anything, or rather, it could mean too many things to narrow down. It's a nickname for names like Jason or Jacob, it's the name of a bird, apparently in Sanskrit it means "victory", it may be related to a romance language word meaning "happy", and so on.
Leon is pretty clearly related to the Greek word for "lion", and Leyon is just a (somewhat silly, if you ask me) spelling variation.
So.. victorious lion? Blue feathered lion? Jason's lion? Happy lion? Your guess is as good as ours.
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