Note: This is a headcanon version of Master Yi, boiled down to the nit-grit for roleplaying purposes. If any lore is not mentioned here, then I'm either unaware of it, or intentionally left it out.
If you feel like there's a piece of lore that would help, send me an ask with evidence so that I may look over it.
Master Yi was once a young child who idolized the swordsman that traveled through his humble village of Wuju, eager to become strong and free of thought like his elders. He trained diligently, so much so that he quickly became known as a 'Young Master' in his own right. These words of encouragement and praise were not enough to sate his desire however, as the infamous 'Wuju Style' was forbidden to be revealed outside of the village's limits. For many years Yi stayed faithful to this golden rule, honing the craft of swordsmanship and poetry alike--
-- that was, until Noxus attacked. With the serenity of his land turned into great calamity, Yi was forced to make a decision that went against everything he held dear. In order to keep the spirit of Wuju alive, he must break his golden rule, and venture into the outside world. Learning of new cultures and fighting styles he's quickly overwhelmed with new knowledge and dangers at every corner. Despite this, he remains hopeful, disciplined, and faithful to his craft, for as long as he draws breath, Wuju lives on.
For the foreseeable future, Yi's goal is to learn of new cultures, comparing and contrasting them to the culture of his people. He hopes that through this he can learn something that will make his style better and more refined, so that he'll be able to more easily teach his disciples-- whenever he finds one.
Your character - through the seven lens of insight- proves to be someone Yi can hone into a disciple of Wuju
Your character guides Yi through foreign lands, helping him remain safe in a world he's not used to.
Your character -- aware of Yi's existence and infamous Wuju style -- wishes to battle him.
These are the only hooks I can think of for now, but feel free to send asks suggesting more!