I think Tywin is pride, not Jaime. Jaime always came off as the least Lannister-like of the Lannisters. He obsesses about making the Lannister name seem good, feeds his ego constantly, and to top it all off he dies at the hands of the man who hurt his pride the most, in the most undignified position. Lysa likewise is killed by someone who's turn to evil was started by jealousy over the woman he was never able to have