It isn't true, not really.
In fact, the last thing Klaus wants is to run underground into who knows what. If he hadn't been able to get her to stop, maybe. But given the choice? He'd rather not.
But to lessen the tension, maybe make Estraeah less angry with him, he would go along with it.
She clearly doesn't believe it. She leans forward, eyes squinted, scanning his face. Her hands are on her hips.