It's on the website. Here's some examples:
http://gameinfo.euw.leagueoflegends.com/en/game-info/champions/fiora/#champion-lore
http://gameinfo.euw.leagueoflegends.com/en/game-info/champions/illaoi/#champion-lore
http://gameinfo.euw.leagueoflegends.com/en/game-info/champions/poppy/#champion-lore
http://gameinfo.euw.leagueoflegends.com/en/game-info/champions/thresh/#champion-lore
Right now the game and the lore are not tied together and Riot doesn't intend to tie them together. The game itself is reflective of the world these characters live in; the maps are locations in Runeterra, the items are objects you'd find in the world, the champions are people of varying walks of life from all across Runeterra, but the gameplay isn't canon. Lyte and Greyor aren't beholden to constant skirmishes on the Howling Abyss, no living people are ever on the Shadow Isles to battle in the Twisted Treeline, Summoner's Rift is basically a ruin in a remote part of the world.
The mantra I follow for what's canon right now and will continue is that everything from 2014 on wards is canon, and the vast majority of 2013 stuff is still canon too. The only thing that's a bit iffy is Maokai's 2013 lore because there's a tiny bit of inconsistency there, but otherwise it's pretty much fine. From then on things get dubious, especially when considering that we're getting a bunch of Mount Targon lore soon, which might throw some curve-balls in the mix as to what we know about Diana. So yeah, 2013 on wards. That's what I go by at least. Any story stuff that is released from here on out can be considered canon and if it conflicts with old stuff, then that old stuff is probably out, however omissions of details doesn't mean things are gone forever; Gangplank's long lore doesn't mention his father, but Illaoi's mentioned him before, so we know that's still a thing.
So yeah, all new stuff is canon, all 2015 stuff is canon, all 2014 stuff is canon, and I'm like 99% sure all 2013 stuff is canon. Take that for what you will.
