Stark tells Jory to ride ahead with his daughters. He'll ride after them. It's definitely time to get out of town. But before this eminently sensible plan can be put into action, Littlefinger comes by to tell him that Robert's been shouting the word "treason" a lot. However, if Ned's willing to wait around until after nightfall, Littlefinger will take him to see the last person Jon Arryn saw. Ned doesn't think he has time. I think even if he has time, he should stop worrying about who exactly killed Jon Arryn and start worrying about himself. And it seems for a second that he's going to do that, but then he tells Jory to put all their men at the girls' bedchambers.
"You bring him without permission. Lysa Arryn is angry at Catelyn for bringing Tyrion to her castle without permission. Everyone's a little thrown by the fact that while Lysa's sitting on the throne, she's breastfeeding her son, who looks to be eight or nine years old. And he might be a halfwit, too. She gets kind of distracted and starts talking about what a good, strong boy her son is going to be, and Catelyn tries to get her back on topic. She reminds Lysa that she's the one who was sending letters around warning her about the Lannisters, but Lysa now says that was a warning to stay away from them, not an invitation to kidnap them and bring them over for tea. The young Arryn observes that Tyrion is little. Lysa agrees with him and tells him that Tyrion is the Bad Man who killed the Hand. Trion, who seems to be having trouble taking this seriously, observes that he must have been very busy, what with all the people he apparently killed. He also mentioned that his brother Jaime will probably wreak terrible vengeance on anyone who harms him. The kid freaks out, and Lysa declares that no one's hurting her baby. The kid calms down enough to say, "Mummy. I want to see the bad man fly." Even Catelyn, who is consumed with the need for revenge, has noticed that this place is ruled by some unstable weirdoes, so she makes a point of saying that Tyrion is her prisoner and shouldn't be harmed. Lysa has Tyrion thrown in a prison cell. And the Eyrie has an unusual dungeon, it turns out. Instead of being underground (and populated by manticores and dragons), the cell is cut into the side of the mountain. So there's no wall opposite the door. It just opens up to the sky. And it's so high, the sky is practically below the floor. Creepy.