For the sake of posterity, here's the rule (from Woe is I--best grammar book in existence):
If you can drop the clause and not lose the point of the sentence, use which. If you can't, use that.
A 'which' clause goes inside commas. A 'that' clause doesn't.
Though you've already used it as you've chosen to use it, according to the 'rule', it should be 'that' if you are separating it into two sentences.
I think your problem came from splitting it into two sentences, but liking the flow of a continuous sentence. It could have (properly) gone two ways:
Carl believed she'd cheated, lied, and left without so much as a goodbye. That wasn't the truth at all.
or
Carl believed she'd cheated, lied, and left without so much as a goodbye, which wasn't the truth at all.
That said, it's your call, of course, and you made it, which is fine. (like how I got both that AND which into one sentence? Mad skills, eh? <g>) You know how it should go in YOUR story. Defend it to the death--unless, of course, you're up against a copy-editor or editor who insists otherwise. Then I say, let the Wookie win, R2.