Liz was happy that their food arrived, and she hoped that it will provide a temporary distraction.
She knew what Max was doing, and even though she would prefer to avoid conflicts and have lunch in peace, she also knew that Max was right. What was the problem in Dr. Snow acknowledging that he knew how she will be presenting? When someone you know is on the stage, it brings a sense of familiarity and it's not shameful to say that one is supporting friends and coworkers. It would not be a big deal if he didn't try to conceal it clumsily and now it really appeared like he had a hidden agenda for coming here.