I think sociopaths indeed do not care whether you know whether they’re lying or not
Sociopaths sound totally convincing even when they recount something that they know is a lie—and even when they know that you know it is a lie. James Fallows points out this clear example.
This goes beyond narcissism, it seems to me, into sociopathic territory: people like this seem to lack the internal alarm signals that a normal person experiences when telling a lie, especially a lie that the person hearing it knows is a lie. Those who feel no qualms seem to be morally blind/unaware, in effect, like a person who cannot feel physical pain, except this sort cannot feel moral pain and cannot understand why lying to someone (even when you know that they know you’re lying) would be seen as any sort of problem. If challenged on it, I imagine such a person would say, “Isn’t that what everyone does? I’ve always assumed so. It’s certainly what I do. Why not?”