MillennialDawn: He’s an especially gifted liar.
The most effective liars are the ones who are convinced that they are being honest. Not about every detail, but about the overarching narrative. I think Evans can lie convincingly because he is certain that he is a good person and a good family man. He is certain that he didn't do anything too terrible, and that he made amends. Thus, he is also certain that he is being unfairly persecuted by people jealous of him.
Any lies he tells are in service of what he believes is true, and so he can lie without guilt or remorse. When he lies to his supporters, it's not like he's really lying- they just need to understand what is going on. When he lies to his family, it's not like he's really lying- they're being unfair and he's just fighting fire with fire. When he lies to everyone else, it's not really lying- and besides, the public doesn't need to know any of this stuff, so what difference does it make?
The most effective liars lie to themselves the most.