Ezreal is the closest anime- looking character I can find..

Simon the Driller
Rides on Lagann to fight, like Rumble.

Passive: Fight the Power
Gurren gains bonus AD for every enemy champion in an area around him.

Q: Pierce the Heavens
The Laggan's next auto attack will drill through the target's armor, reducing it for a few seconds. The armor shred is increased while in Gurren Lagann form.

W: Spiral Power
Simon gains increased confidence in himself, empowering the Lagann giving it bonus damage and attack speed. This can be stacked with Gurren Lagann's Spiral Power.

E: Cannonball Special
Laggan shoots itself head first at an enemy, causing damage to the target and anyone that Lagann passes. Damage is increased during Gurren Lagann form.

R: Giga Drill Break
Lagann fuses with Gurren, creating the Gurren Lagann and using their signature move on an enemy target. The target and all enemy units in an area around them take physical damage and have their armor reduced. Lagann remains transformed for a short duration after using this spell, giving him a longer auto attack range and Spiral Power. His spells gain a bonus if used in this form.

Haruhi Suzumiya

Role: Viable as both AD and AP, with the AD counterpart being a tad more popular.
Haruhi is based off short-cooldown skillshots, which is why rushing a Trinity on her is a viable idea.

Passive : Rising Spell Force
Hitting a target with any of Haruhi's abilities increases her attack speed by 10% for 6 seconds, this effect stacks up to 5 times.

Q : Mystic Shot
Haruhi fires a bolt of energy in a line that will deal physical damage and apply on-hit effects to the first enemy it hits. If it strikes an enemy unit, all of Haruhi's cooldowns will be reduced by 1 second.

W : Essence Flux
Haruhi fires a wave of energy in a line. Any enemy champions it passes through are dealt magic damage and have their attack speed slowed for 5 seconds, while any allied champions it travels through have their attack speed increased for 5 seconds.

E : Arcane Shift
Haruhi instantly teleports to a nearby target location and fires a homing arrow at the nearest enemy unit, dealing magic damage to it.

R : Trueshot Barrage
Haruhi channels for 1 second to fire a powerful broad energy missile that travels in a line across the whole map and deals magic damage to each enemy unit they pass through. It will deal 8% less damage for each subsequent target hit, down to a minimum of 30% damage dealt.

Did I do it right?

Noel Vermillion

AD-carry

Passive-Chain Revolver: Noel wields her guns with intense precision and skill, and activates Chain Revolver after every shot, which increases the damage of her next skill. A full charge of 6 shots grants an additional effect.

Q: Revolver blast: Noel swings her revolvers and quickly fires a shot that can be used 3 times before cooldown, the last shot knocks opponents up slightly.

Full charge effect: Revolver blast can be used 6 times before cooldown, the 3rd and 6th shot knocks opponents up slightly.

W: Optic Barrel: Noel dashes to a location and fires a single shot that marks an opponent. Marked opponents take more damage and have their attack speed and movement speed decreased, which slowly regenerates over time.

Full charge effect: Enemies that are marked can be seen even when out of range.

E: Nemesis Stabilizer: Fires a powerful laser shot that knocks noel back.

Full charge effect: Nemesis Stabilizer's laser is granted incredible range.

R: Mu-12: Noel releases her emotions and transforms to Mu-12, Her revolvers turn into huge floating swords. As Mu-12, Noel is granted AD and ignores a % of an enemies defense. she is granted full charge until she turns back into Noel form. She is able to summon Sword of the Godslayer, which slams down onto a large area and stuns enemies caught in the center.

Noel is basically a AD caster carry with a reverse sheen effect.

Yes. Must make Noel OP. But seriously, if a champion was released like that...lolll.

Azuma Kazuma

OP Baker, probably friendly with Leona because he has the Solar Hands.

Q: Bakes Bread that will put the opponent into a delirious reaction.
W: Bakes Bread that will summon legendary beasts that are actually figments of the opponent's imagination, nevertheless they deal BREAD DAMAGE.
E: Bakes Japan #44 that is so good it kills you... temporarily.
R: Revive a teammate by sending them back in time to rescue their own parents and probably removing appropriate champions from the League.