Catching her in a lie and rubbing her nose in it doesn't help your cause.
Neither does being a doormat. If she blatantly lies to you, there is nothing wrong with you letting her know that she lied. Try not to take it personal though. People don't respect others who let them treat them like doormats.
"Always go straight forward, and if you meet the devil, cut him in two and go between the pieces." - William Sturgis, clipper ship captain, 1830's.
