The Ziggurat and the "petite" lie

There's something very strange at the end of "The Ziggurat." Emery is trying to lie his way out of trouble and he tells the police that "Tamar" is an exchange student who is staying with them. A little later he says: "My wife calls her petite." The lie came easily, unbidden. What's going on here? He's telling a lie his wife can contradict. That might make sense if they had a loving relationship and could collude beforehand, but they are adversaries in a divorce case. Another possible explanation is that he knows his wife and kids are dead. So do we need to dust off the Maximum Delusion theory I've seen in the archives?

It looks like he just isn't thinking clearly, which is understandable. He doesn't believe his wife is dead, because he whispers to Tamar that his wife will not want a divorce after she learns of the new company. Tamar is asleep and doesn't understand everything he says, so there is no reason for him to lie to her.