LoreKai Munaro was born the child of beggars, living off of gold pickpocketed from wealthy Demacians as they passed. Kai was a dreamer, and even as a small child he dreamed of great things. He heard tales of mages bending the arcane to their will, and was entirely enthralled. He decided that someone must be able to give him those powers, if only he could find this person and have enough gold to pay. It did not breach Kai's 9-year-old mind that he simply was not born with the gift of magic, but that did not stop him from trying. He used every trick in his already formidable book to steal enough gold, but he had no way of knowing how much would be enough.
Sixteen years later, Kai still had not given up on his dreams of becoming a mage. He had the underworld of Demacia wrapped around his finger, but he would give it all up in an instant if it meant realization of his quest. When Kai caught wind of a priceless magical artifact held in the Institute of War, he knew that this may well be exactly what he had been looking for all those years. Kai didn't have a choice; his wildest dreams were finally within arm's reach; he couldn't resist taking the chance. Kai nearly became the first thief to successfully steal from the League of Legends, but as he made his exit he found himself surrounded by guards. Kai couldn't fight his way out, so he did the unexpected: he tapped into the full arcane energy of the artifact, flinging the guards about like ragdolls. While he couldn't escape in time to avoid imprisonment, the League's summoners were impressed by his display of magical aptitude and offered him a deal: work for his freedom by becoming a champion on the Fields of Justice.
Kai's mediocre AP scaling and self-dealt magic damage make Abyssal Scepter possibly the single best item for him. The MR reduction helps him deal much more damage while the MR reduces the damage he deals to himself. Lich Bane is great on Kai as well due to his low base cooldowns and the fact that he deals the majority of his damage in autoattack range. For the trinket, it's a toss-up between Warding Totem and Scrying Orb. Warding Totem is a far more useful trinket for the team, but use of it reduces Kai's own mobility with his E. On the other hand, Scrying Orb sucks.
Kai is intended as a midlaner. He functions as an anti-mage assassin similar to Kassadin with a Diana-like ult. He is extremely sticky and extremely slippery, with only one ability that is not a dash or blink.