While Jaime didn't know about it, Tywin's talk with Tyrion afterward made it clear that this was as much Tywin's decision as anyone else. Plus, the Rains of Castamere was a song about the Lannisters, Roose's last words to Rob was about the Lannisters, we know the Lannisters were allied with and plotted alongside the Frey's, etc. The whole event was made to remind the North what happens when you cross the Lannisters, so not a huge leap to connect Jaime-Robb's former prisoner-to the whole thing. Of course Joffrey didn't know. He was largely kept out of the loop.Jamie had nothing to do with the Red Wedding. He was not aware of it. There are two ways to interpret the "regards" comment. I see it as Jamie sending a message to Robb that he is now free and no longer his prisoner and a "nyah, nyah". Book readers see it as a 'nyah nyah' to Roose because he's loyal to Robb, the usurper, and Jamie telling Roose to send his regards, is like Jamie saying "Go tell your boss that I'm free", a dig that Roose is an underling. At that point, when Jamie and Roose speak, the Boltons are still loyal to the Starks. Jamie had no idea what was being plotted.
Tywin, at most, sanctioned it. I like to think Roose floated the idea of a way to kill Robb and Tywin of course is all for it. The Lannisters as a family, had little to do with the Red Wedding, Remember in the episode following the Red Wedding, there's a small council meeting, discussing it, and Joffrey is excited to hear the news. There is no implication that they expected it to happen.
At most, Arya's list, is people who she has witnessed do her or her friends and family harm. Jamie hasn't harmed anyone she knows, that she knows of, Bran being the exception.
In any case, the fact remains, Jamie is not on Arya's list. She wouldn't kill him, unless Bran shows up and says, "Jamie pushed me out of the window"
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