The thing is, if she knows that, why isn't she constantly at his elbow watching him? Because Klaus is VERY dangerous, and he might yet find a way to defeat her if he can twist things enough. I suspect rather that Lu is convinced that Klaus is as much her slave as any normal revenant - her ego would demand no less - and she's gone off somewhere to gather the Other's forces, leaving Klaus to finish Agatha.
She may be in for a surprise when she gets back...