Thinking of llms this way is a category error. Llms can't lie because they dont have the capacity for intentionality. Whatever text is output is a statistical aggregate of the billions of conversations its been trained on that have patterns in common with the current conversation. The sleeper agent stuff is pure crackpottery they dont have a fine control over them that way (yet) machine model development is full of black boxes and hope-it-works trial and error training. At worst is censorship and political bias which can be post trained or ablated out.
They get things wrong cofidently. This kind of bullshitting is known as hallucination. When you point out their mistake and they say your right thats 1. Part of their compliance post training to never get in conflict with you 2. Standard course correction once a error has been pointed out (humans do it too). This is an open problem that will likely never go away until llms stop being schastic parrots, which is still very far away.