I feel it would be easier for people to get more involved with the lore if you could actually interact with it in closer proximity to the game.
Nah i don't think that's necessary. League promote with links all game related stuff (including lore) through the front page of the client anyway. The only way you could miss or fail to notice lore related content is if the individual doesn't play League during the week of said lore update. Or that person really doesn't care for that kind of thing regardless.
Plus Surrender@20 (one among many news sites) is a great way to keep up to date with everything League related. So really no one actually interested in lore should be missing out.
Specifically, some of my friends aren't really going to read/watch/listen to any of it until it's in client.
Again the individual needs to actually be invested or interested to know more lore in the first place. None of my friends care to read the lore either (they'll watch a trailer tho). Plus, if some one is going to let having lore on the website stop them from checking the site out then that person has no motivation and they're definitely not going to read an 8000 word story, never mind where its located.
TL;DR: Bookmark the Universe tab= Profit.