Ah! Some dead people in a courtyard! How exciting. As we pan up, it appears that we're looking at Harrenhal. Harrenhal has a lot of picturesquely melted stone towers. Then camera eventually makes its way up into Tywin's chamber. Tywin looks at the dart that killed Amory Lorch and says that it's wolfsbane. From that he deduces that it was no ordinary assassin. Or maybe Amory Lorch was a werewolf! The Mountain says they hanged twenty men the previous night in an attempt to scare away assassins (or something; he doesn't really explain what his goal was), but Tywin doesn't care: "The man tried to kill me. I want his name, and I want his head." Seems reasonable. Although it seems like Tywin wasn't actually the target of the assassination. I think it was Amory Lorch, because he's the one who's dead now.
The Mountain says they think it was an infiltrator from the Brotherhood without Banners, whoever they are. Tywin is vexed, and wants them all dead. The Mountain says it will be hard to find them. Tywin says to just burn all the villages and farms in the area. See, that seems like an easier plan than all this person-by-person interrogation. Arya lays out some mutton and appears to consider stealing a knife. Tywin says he doesn't like mutton, but has her leave it. He tells her to eat, and she wants to eat in the kitchen later. He tells her, "It's bad manners to refuse a lord's offer. Sit. Eat." She does. He tells her she's small for her age, but she assures him she eats a lot. Now he's in a contemplative mood and turns toward the window. He says this will be his last war, win or lose. And of course, he's never lost. He says it's already being called the War of Five Kings (Joffrey, Robb, Renly, Stannis, and... Balon? I guess he's known publicly now that Theon has Winterfell), and his legacy will be determined in the coming months. Arya considers stabbing him in the back.