You can analyze a lie only if you know that the speaker is trying to convince you into performing an action. Binary statements about facts cannot be judged without knowing the truth. They could be used only for self-analysis of the analyzer and maybe if you want to exercise some tail chasing.
Watch The Princess Bride and you will find a wonderful scene about choosing the right cup there.
von Neumann proved that you can extract fair results from a biased coin without knowing the bias. No truth needed.
While it doesn’t really apply to this situation, it’s all to say that i disagree with you saying there’s only information in the truth.. There’s information in everything.