Why Isn't the lore team doing their job?
Well their job is to write lore. They got Burning Tides out so they have done their job recently. Can't speak to this right at this second but they DO seem to be doing their job: write lore.
Why Is the team dedicated to producing quality lore talking to players about less than people from other teams?
Presumably because they're busy working on said lore.
Riot's lore/narrative/foundations team doesn't seem to know what it's doing.
Where do you get that from anyway? I'd understand this pov if you were debating what they were walking about but you've come in here saying "Why aren't they talking? They don't know what they're doing" which seems like a statement that's counter to itself.
It's making me lose faith in Riot as a company.
Making you? You mean you still have faith? I'd assumed from your spam that you'd lost faith a long time ago.