Let's see, I've read all of the bios. I see no reason not to & it gives me taste of who the champs are (from the narrative perspective). That said, I don't really re-read them. While I know all the major stuff about the champs backstory & even some mid level stuff, don't except me to know all of the minor details.
I honestly don't bother with the color stories unless it's a champ I'm personally invested in. Short stories I tend to skip to, unless it involves champs I like. Short stories are one offs most the time with no major changes I need to concern myself with.
Long stories, or stories with multiple parts, like Burning Tides,Shadows & Fortune,Bloodlines & Confessions of a Broken Blade are stories I read. For one, they're not one offs. They feature major events for a number of the champs.
I've read all of the comics & watch all of the cinematics/animations. I'm more of a visual guy, so I'm willing to indulge in those even if they're not about my favorite champs.
Do I know everything about the lore? Nope. Do I know all of the major stuff & basic elements? Yes, or at least I got a good idea of it.