I'm not a psychologist either and my opinion isn't as a professional,but rather an amatuer."Wouldn't a true sociopath be able to lie without getting angry about it?"Good question.Maybe/maybe not.They experience anger just like us.They're also consumate actors,so if "anger"is appropriate at the time......
If you want to play armchair shrinkologist, the way to go is to understand that their entire ego structure, the story they tell themselves about who they are and how they fit into the world, is at stake and, as they see it, to lose would be worse than death. So they HAVE to fight for their version of reality. It's life or death for them.