The concept that Jaime will lie to save his own skin
Jaime is a lot of things, but a liar is not one of them. He doesn't broadcast his business to everyone, but I don't believe there is a single example of Jaime lying to a direct question at any point in the story -- even when Robb accuses him of sleeping with Cersei he asks for proof instead of denying it.
@Constantinople -- I don't really understand the need to cast someone in a good/evil light when it's clear the character isn't meant to be viewed in that way. Obviously that's your right, but Jaime has done both good and evil in his life and trying to simplify his actions by labeling him as an evil character is misleading. You're rather persistent about the bathhouse scene but there's no evidence to support that reading, and you were adament, IIRC, that he would not return for Brienne, or was lying to her for the purposes of getting her to let her guard down. In reality, he risked his own life to save hers, so clearly the idea that he was simply manipulating her and she means nothing to him has already been disproven and will likely continue to be disproven in this upcoming season.
Again, this is not an attempt to excuse all of Jaime's actions (I think some defenders go a bit far in justifying his actions with Bran), but to simply label him as evil I think is a gross mischaracterization. He's done evil things at points in his life, but it's willful dislike of the character to say he didn't grow and/or change through his interactions with Brienne. I think, personally, that he's in the process of becoming a better man (doesn't make him a "good guy" either), and that hopefully such development will continue.