For Lacan, it is not enough to claim simply that truth is unconscious. Although this is certainly a correct view, it nonetheless needs to be submitted to an altogether more difficult position. And this was one of Lacan’s interesting correctives to the traditional Freudian notion of truth: truth, in the unconscious, is produced as a consequence which anyway ends up being followed and determinative of the subject’s desire.
For example, in Lacan’s 18th seminar he wrote: “[something] is only true by its consequences, like every oracle. Interpretation is not put to the test of a truth that can be settled by a yes or a no, it unleashes truth as such. It is true only in so far as it is truly followed.”
For Badiou truth is connected at some level to being but it nonetheless comes after, through torsion of the world of appearance with the world of existence. This is perhaps what Lacan meant when he said in his first seminar that “Truth hollows its way into the real thanks to the dimension of speech. There is neither true nor false prior to speech.”