I always took that scene to mean that the Archbishop was in on the poisoning of Lamberto. To what extent we'll never know, but it seems he's looking down into his own tea much the same way as a murderer might stare at the gun or the dead bodies for a split second after the act. He's either thinking how easy it to kill someone and worried his next cup of tea could be his last or else he's relieved that his cup of tea is poison-free.