Tywin Lannister died without any other heir than Tyrion Lannister and his young wife Sansa, and rather than continue the mad fighting in Westeros Tyrion severed all ties and declared Casterly Rock neutral until a single King sat unquestioned on the Iron Throne. The fighting still continues, but House Lannister now takes in war orphans who are raised by Lady Sansa--it is this custom that first draws Daenerys Targaryen to Casterly Rock.

Tyrion knew, as he gazed up at the dark skinned Martell man that this was perhaps his only chance to spirit Sansa out of King's Landing and away from his father's greedy fingers. Tywin Lannister would have married the girl himself if he felt he could have gotten away with it, and so Tyrion knew his own marriage was no protection to Ned Stark's daughter whatsoever. "Invite her, demand her, steal her--whatever you choose, Prince Oberyn, choose it soon. Else my lady wife shall break into more pieces than the stars."

“I slept fine enough,” Jaime grins back. “And I’m sure your daughter won’t have my head for anything that’s happened in the last moon.” “That she won’t,” her father agrees. “And please, the last thing I dared hope for her was that she’d marry someone who would just care for having heirs and not even knowing them. All things considered, I think any woman in the realm would kill to have you for a husband.” “Just everyone’s luck that she waited long enough to run into me, right?” Or: in which Brienne is off being a knight in shining armor and Jaime is in no way shape or form stopping her from doing it.

Jaime Lannister drives her sword through Aerys's back to save a kingdom. When her father's armies sack the city and kill those she was sworn to protect, she flees King's Landing, unsure what to do. On her way to Dorne, she runs into Ned Stark who hands her a baby and a purpose, protect the Targaryen heir. A Jaime Lannister redemption story.