A luthe is a half truth and a half lie. Normally used when one does not want to divolge the entire truth to another (normally loved or favoured) person. It includes telling a half truth based on a statement the person made. It is used to "protect" the person, normally because they are excited, proud, happy, etc, but you do not entirely agree with their point of view or opinion, so you agree with their ideals, momentarily, even if that is not how you feel, all for the sake of spearing their feelings.
Carly and Nick are girlfriend and boyfriend. They are currently riding together when a Linday Lohan song comes onto the radio.
Carly: Don't you just love this song Nick?? I mean it's sooooooo good and like it has an awesome beat!! I love Lindsay Lohan! She's so cool!
(Nick contemplates for a moment, he thinks the song is really kewl, but he HATES Lindsay Lohan. He diecides to luthe.)
Nick: Um, yeah, this song rocks! And, um, so does Linday.