I can help with this, though full disclosure: I'm currently doing work on the NA team, so this process likely has changed.
An example of lore I can give are the faction breakdowns - we'd start by setting a meeting for, say, Noxus. Then the team would get together in one of the more spacious conference rooms (it had a bean bag chair at one point) and break down what the current state of the faction's lore was. Main players? Important figures? Politics? History? Society? Future? We'd go through what existed, read some of the adjoining champion information, then begin a multi-week long series of meetings brainstorming what defined the places and people that make Noxus, well... Noxus.
On top of that, there were per-week short story submissions for everyone on the team, and those would go through rounds of critique to flesh out the most vibrant and cohesive vision of Noxian society/champs. During this period we'd also double up by having Noxus champion breakdowns, so we'd be simultaneously looking at, say, Katarina, while also looking at how and where she was raised and why. She would also have short story submissions during that time, which tended to include Cass, Talon, and her parents. After a while we'd feel comfortable enough to move on to another faction, so that we could cycle through them all until we ended up at Noxus for another round of iteration.
It was super fun, but also a TON of work. I have mad respect for those guys. In any event, hope that helps!
