Some weapons/tools I think would be pretty cool on a league champion.
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an ATV A character who has a car could be pretty cool. He would probably drive around, maybe going over small terrain, with the ability to have an ally (or allies) in the back seat, from which they can fire attacks. While the passengers and driver take reduced damage while in the ATV, if the ATV itself takes too much damage, it will explode, and any allies near it will take a big chunk of damage.
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Hair Pretty simple. A champion who ensnares its targets in its own long, flowing locks. Just a random item.
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A first aid kit/medicine We have healers, yes, but we don't actually have any doctors in the game (except for Heimerdinger, who isn't a medical doctor. I don't count Shen/Kennen/Akali).
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Razor Wires Have you seen Hellsing? Remember Walter, and how much of a badass he and his wires are? Yeah.
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Bullwhip Could be a fun character. Using some kind of whip, this champ goes all Indiana Jones on us. A mid range basic attack with a passive that causes his autos to stop the movement of his target momentarily. One ability would be a skillshot that brings the first thing it hits to our Indy impersonater; friend or foe. If not that, it could "steal" from them, stealing stats from their most expensive item until Indy died.
You guys have any other ideas?