The following champions have had their main lore updated or newly made in the current format, which is a long bio with a short story accompanying it. These are the most reliable sources of lore that exist for champions at the moment:
Graves, Gangplank, Twisted Fate, Miss Fortune, Fiora, Kindred, Mordekaiser, Karthus, Kalista, Thresh, Hecarim, Illaoi, Poppy, Jhin, Shen, Leona, Diana, Pantheon, Aurelion Sol, Taric, Azir, Xerath, Nasus, Renekton, Skarner, Sivir, Amumu, Rammus, Taliyah and Ryze. Kled will have full lore when he's released and Yorick is also going to have his lore updated this year.
The following regions of Runeterra have had lore about them put out in a big way:
The Freljord, Bilgewater, the Shadow Isles, Mount Targon and Shurima.
The League of Legends and the Institute of War aren't canon in the lore anymore, and so any references to that in the lore aren't canon or at least aren't entirely factual sources of lore anymore.
That's a basic guide to what's good to look at and what isn't. I could get super technical but I'll just give you this for now.