Withholding, prevarication and lies

What happens when a character doesn't offer up their knowledge about a situation, twists it somehow, or outright lies? Not only does their reliability come into question, but a mystery is created. Why did the character do this? What's the truth of the matter? When will it be revealed, or will it ever?

In The Turn of The Screw, the Governess holds a good deal of information back — from Mrs. Grose, the housekeeper; from the children; from her employer (who instructed her to do exactly this, bother him about nothing, no matter what); and from the reader. She also occasionally lies about what she has seen and heard.  In Katie Kitamura's Intimacies, a character pretends to have a short-term amnesia after an assault, but the protagonist suspects he is faking it. When does prudence or circumspection fade into falsehood? It's a murky but tantalizing line, and one that creates great tension, narratively, because it keeps us guessing about the story, which is to say, actively engaged

PROMPT: Introduce some level of falsehood into a character's relationship with either another character or the reader. It could be an outright lie or simply the allowance of a misperception. It could tie into a major plot point or be something more peripheral, but use it to complicate our understanding of the liar’s character.