No, not usually. It would depend on what it is. If it's harmless stuff, who cares. If it's detrimental to a relationship I'm more inclined to leave than bother. Don't you love when someone is lying and you know?
When you know someone is lying do you point it out?
Not as a rule. I don't like liars and can't be bothered arguing with them. They're not worth the effort. On the other hand I have been known to drop the occasional expletive if they persist. "Bullsh1t!" covers it pretty well.
Sometimes, or sometimes I lay the foundation to catch them in a lie to the point that they confess. :)