This isn't really true. Saw it mentioned on twitter than Vardy's average position was much further up the pitch than it has been, because he was staying on the last man even when Liverpool had the ball. Which is a small change, but it got them the first goal. Also might imply that he's working less hard, by not pressing.
I dunno. I can believe the story that they gave a less than enthusiastic response when the directors asked them about Ranieri last week. Which was probably the right thing to do. They're employees of the club, not Ranieri, so it wouldn't be right to pretend everything is fine just to protect Ranieri.
However, I don't really buy that they "weren't trying". I know it happens, but I don't think it happened here. You see their game against United, for example, where they scrap really hard for 40 minutes, concede one, then immediately concede two more. That to me doesn't look like a lack of effort, it looks like a psychological issue.