Every champions has its own lore, here are a couple of them.

A vicious Void predator, Kha'Zix infiltrated Valoran to devour the land's most promising creatures. With each kill he absorbs his prey's strength, evolving to grow more powerful. Kha'Zix hungers most to conquer and consume Rengar, the one beast he considers his equal. When Kha'Zix crossed over into this world, he was fragile and ravenous. The animals he first encountered were too small to fuel the rapid evolution he craved. Kha'Zix focused his hunger on the most dangerous creatures he could find, risking his life to satisfy his need. With each kill he feasted and changed, becoming a stronger, faster predator. Kha'Zix soon chased his prey with unrestrained aggression, believing he was unstoppable. One day, while savoring a fresh kill, the predator became the prey. From cover a creature pounced in a blur of fangs and steel, tackling him to the ground. It roared in his face slashing and clawing, and Kha'Zix felt his blood spill for the first time. Screeching in fury, he sliced at the brute's eye driving it back. They fought from sunset to sunrise. Finally, near death, they reluctantly separated. As his wounds closed, Kha'Zix burned with anticipation at the idea of devouring one who could match the Void's strength. He resumed his search for powerful prey with renewed vigor. Someday, Kha'Zix will feast on Rengar.
"Kill. Consume. Adapt."
- Kha'Zix.

Unlike other foxes that roamed the woods of southern Ionia, Ahri had always felt a strange connection to the magical world around her; a connection that was somehow incomplete. Deep inside, she felt the skin she had been born into was an ill fit for her and dreamt of one day becoming human. Her goal seemed forever out of reach, until she happened upon the wake of a human battle. It was a grisly scene, the land obscured by the forms of wounded and dying soldiers. She felt drawn to one: a robed man encircled by a waning field of magic whose life was quickly slipping away. She approached him and something deep inside of her triggered, reaching out to the man in a way she couldn't understand. His life essence poured into her, carried on invisible strands of magic. The sensation was intoxicating and overwhelming. As her reverie faded, she was delighted to discover that she had changed. Her sleek white fur had receded and her body was long and lithe, the shape of the humans who lay scattered about her. However, though she appeared human, she knew that in truth the transformation was incomplete. A cunning creature, she adapted herself to the customs of human society and used her profound gift of beauty to attract unsuspecting men. She could consume their life essences when they were under the spell of her seductive charms. Feeding on their desires brought her closer to her dream, but as she took more lives, a strange sense of regret began to well within her. She had reservations about actions which never troubled her as a fox. She realized that she could not overcome the pangs of her evolving morality. In search of a solution, Ahri found the Institute of War, home of the most gifted mages on Runeterra. They offered her a chance to attain her humanity without further harm through service in the League of Legends.
"Mercy is a human luxury, and responsibility."
- Ahri.

When the prophet Malzahar was reborn in Icathia, he was led there by an ominous voice which thereafter anchored itself to his psyche. From within, this voice bestowed upon him terrible purpose, and though Malzahar was no longer tormented by its call, the voice did not cease its unrelenting summons. This baleful beacon's gentle flicker - now fastened to Runeterra - drew forth a putrid beast that ambled across a threshold it did not understand, widening a fissure between spaces which were never meant to meet. There amongst the haunting ruins of Icathia, Kog'Maw manifested in Valoran with unsettling curiosity. The spark which led him to Runeterra teased him still, urging him gently towards Malzahar. It also encouraged him to familiarize himself with his new environment, to the stark horror of everything he encountered on his journey. The enchanting colors and aromas of Runeterra intoxicated Kog'Maw, and he explored the fruits of the strange world the only way he knew how: by devouring them. At first he sampled only the wild flora and fauna he happened across. As he traversed the parched Tempest Flats, however, he came upon a tribe of nomads. Seemingly unhampered by conventional rules of physics, Kog'Maw consumed every nomad and any obstacles they put in his way, amounting to many times his own mass and volume. The most composed of his victims may have had time to wonder if this was due to the caustic enzymes which stung the ground as they dripped from his gaping mouth, although such musings were abruptly concluded. When his wake of catastrophe reached the Institute of War, an enthusiastic Malzahar greeted him with an enticing prospect: taste the best Runeterra could offer... on the Fields of Justice.
"Time to feast."
- Kog'Maw.