Lying is difficult to get across in written dialogue. If the text is too dry, a player is tempted to look at it like a logic puzzle, and I don't think that's the effect you're going for. You're hoping for players to pick up on cues, or intuit, the liar. Empathize rather than analyze.

To evoke that sort of empathy from the player, you need to give them something they can relate to. They don't necessarily need to relate to the characters themselves, but they need details that make them feel one way or another about a person.

If you have a format in which you can describe body language, this becomes much easier. You can say that a person looks nervous, and it doesn't give away whether the person is lying or not. Maybe they're nervous because they're about to be caught. Or maybe they're nervous because the player is all up in their grill, and all but accusing them of some heinous crime they didn't commit.

If you can't convey body language (so if you just have lines of dialogue with no exposition), you've got to convey the same information through dialogue. The more personality you can convey, the better. "Um" is a good word that shows that a person is nervous, for example. Providing flavorful text is also a good way to give players something they can relate to:

JESSE: Hey, Mr. White...hand me a drink, please?

vs.

JESSE: Yo, Mr. White...gatorade me, bitch!

The player is going to make immediate assumptions about someone who speaks like the second version of the dialogue, and you can use this to your advantage to convey information about the character (or mislead them). More importantly, once players know who the characters are, they'll be able to spot lies more easily. The example I use is a cliche, but it's useful for illustration purposes.  Imagine if Jesse suddenly switches from "Yo, bitch" to "Hey, ma'am" - he's not speaking naturally, which means he's watching his words. Is he trying to be respectful, or is he hiding something? It gives the players an intuitive 'in', a way beyond binary logic to determine if characters are lying or not.

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