It's clear which of his kids Tywin likes best given his reaction to the news of Jaime's defeat. It's too bad his idiot daughter cut off the head of the only guy who could have been traded to get Jaime back. While Tywin stews, the Lannister war council reviews what happened at Riverrun. Basically Robb snuck up on Jaime while Tytos Blackwood "took them in the rear." Taken in the rear by some guy named Blackwood -- ouch. Tywin's little council is freaking out, even suggesting giving up. Perhaps Eddard will get his revenge sooner rather than later.
Also, Renly decided to declare himself King and Cersei wants Tywin's army to defend King's Landing. So Joffrey is the official king, but Robert has two brothers (Stannis and Renly) who both want to be king. Do they each have armies? Why don't they work together? Maybe they should have an election. Instead of dwelling on these questions, I focused on the much more important part of this chapter: GREGOR's new assignment of burning the river lands. I sense some kickass GREGOR SMASH action coming up soon. GREGOR even speaks in this chapter, suggesting that they cut the eyes out of every Lannister scout who failed to spot Robb's army. Blind scouts! I like it.
Tywin plans on sending Tyrion to King's Landing because Cersei and Joffrey "lurch from one folly to the next." You see Tyrion? Your father loves you. Or at least respects you enough to know your strengths... especially when his only other son is captured. Tywin gives Tyrion one last command: don't take the whore. It's actually good advice, because Tyrion seems to be falling head over heels for another pretty face who's clearly just after his wallet. But it seems like Shae's coming anyway. Tyrion is such a rebel, taking his personal whore when his father told him "no whores." Maybe he'll marry her, too.
Jon's planning on going south to help his half-brother Robb. Despite all those heart-to-heart talks he had with Benjen, or that blacksmith guy, or Aemon, or LC Mormont, Jon still decided to break his vows to the Night's Watch. Jon reverts into full self-loathing mode, telling himself that he'll never be accepted anywhere. Look on the brightside Jon, you can own land now. And have sex now. Probably both, as one leads to the other. But if he gets caught, he'll end up headless like Eddard.
Fortunately for Jon, his friends show up and convince him to come back with a cheesy oath recitation. Jon returns, and it seems LC Mormont pulled a Varys, predicting that Jon would leave and then come back. Old Mormont gives Jon a stern, fatherly lecture: Jon should stay for a lot of reasons, but mainly because undead invasions are pretty bad. Mormont likes Jon because he realizes the power of giant magical wolves and all that superstitious stuff. Jon obeys, and vows he'll stay. Jon needs an agent, because he probably could've gotten Mormont to allow at least a little sex or land ownage. Not that it would really matter, since the NW is planning on marching north -- a plan that has "disaster" written all over it. Yes, let's take the handful of badly trained guys we have and leave the safety of our gigantic wall to fight supernatural zombies. That sounds like a great idea.