By some twist of fate, Aerys's obsession of Tywin gets into a darker path and he begets children (all Lannister and Targaryen children minus Rhaegar) by Tywin Lannister and Westeros changes irrevocably. Or Tywin is the heir of the Emperor of a forgotten land where shadow binders don't even dare to go there, or in another word, Stygai and beyond that.
"Cersei was there. She was obligated to go where her husband, the Crown Prince, demanded her to go. He humiliated her. He forced her to watch him fucking your bitch of a sister. My sweet sister was cruelly separated from her children. He let their children be defenceless. He left them to the Mad King. Weren't for their dragon blood they would be dead by now.
"So Stark, do us a kindness and never ever speak about honour to us, Lannisters, especially me," says Tyrion, a small man, but his voice carries over the entire field. No one dares to speak after him or interrupt him.
Ned steps back as if he gets punched by the imp's fists onto his face, not by his little speech. He closes his eyes. By Old Gods! Lyanna, what have you done?