Upon seeing him, Clara will motion for L to come in closer, and will occasionally look to him to watch his face for a sign of a reaction. She's expecting him to contribute to the conversation, and is surprised that he doesn't. If anyone asks him to leave, she'll put her foot down and say that she gets to say who leaves and goes.

And since she'll be pressing him for a contribution, she'll inform him that he's fully expected to stay and tell her privately what the other teams are discussing.