One of Game of Thrones' greatest characters met her end on the latest episode. Lady Olenna of House Tyrell was defeated when the Lannisters made their way to Highgarden instead of Casterly Rock, as Tyrion anticipated. Naturally, Jaime found Lady Olenna waiting calmly in her chamber for her death, which surely came. However, some are wondering why did Jaime kill Lady Olenna on Game of Thrones? The simple answer is: because Cersei wanted him to.
Despite many fans' hopes, Jaime is still very much in love with Cersei, which was proven after they hooked up again for the first time in a long while during Sunday's episode. Now that Cersei is queen, she's lost all sense of propriety and doesn't care who knows that she's sleeping with her brother, even though she basically confirmed she'll marry Euron, now that he's given her a "gift."
Anyway, it makes sense that Jaime would do anything Cersei asks, but moreover, it wouldn't have made sense to leave Lady Olenna alive. For one, she was allied with the enemy (Daenerys). Secondly, if Jaime let Olenna go, it would be a direct betrayal to Cersei and he knows that. Also, if you think about it, it was actually a mercy that Jaime gave Olenna the poison to kill herself.
Jaime told Olenna what Cersei would've liked to do with her. She would've had Olenna dragged through the streets and tortured if she was brought back to King's Landing alive. However, Jaime convinced Cersei to let Olenna off the hook and to just give her a painless death. Unfortunately for Jaime, Olenna let him know he shouldn't have.
After she drank the poison, Olenna reminisced about someone else who was poisoned, though his death wasn't painless at all. She was referring to the "Purple Wedding" back in Season 4 when Joffrey was killed and everyone was led to believe it was Sansa and Tyrion's doing. However, Olenna finally confessed to Jaime that it was actually her who killed his son.
Like the original gangster she is, Olenna told him to also pass the message along to Cersei. "I want her to know it was me," she stated in an epic mic drop moment.
Jaime was so at a loss for words, he just walked out, leaving Olenna to die. Though it definitely hurts to say goodbye to Olenna, you have to give her props for going out with the last word. Only she could still leave you wounded, even after you gave her the poison to kill her.