My favorite recent lie was a FOX terrorism "expert" asserting that parts of Birmingham and Paris were no-go zones for non-Muslims. A lie that has since been forwarded on right-wing sites and by the likes of Bobby Jindal. The expert spent considerable time braying about this but later tweeted an apology...because guess what...it's not true. Of course FOX didn't or hadn't yet corrected that lie.
American's Against the Tea Party has a list of FOX lies.
There's this too from the Tampa Bay Times
This scorecard shows the ratings for statements made on air by Fox, Fox News and Fox Business personalities and their pundit guests. Rulings do not include statements made on air by politicians or paid spokespeople.
Fox 'Expert' Lies About How You Can Catch Ebola
Another FOX lie tracking site
Inside the Fox News lie machine: I fact-checked Sean Hannity on Obamacare