Underestimating the Lannisters is never a good idea and Cersei and Jaime proved that more than once during "The Queen's Justice." (The episode name itself should have been a tip-off, eh?) After the Lannister army overtook Highgarden, Jaime killed Olenna Tyrell on Game Of Thrones by giving her poison to drink. But Diana Rigg's badass grandmother character was able to unveil one last secret before her death — that she was responsible for poisoning Joffrey. Cersei's hatred for her younger brother Tyrion is so strong that she always assumed he was the one who killed Joffrey during his wedding to Margaery Tyrell. But the Queen of Westeros is about to finally learn the truth since the Queen of Thorns specifically stated that she wanted Cersei to know that she was responsible. And while Olenna is already dead, meaning no more revenge can be exacted against her, Cersei knowing that Olenna killed Joffrey could maybe — just maybe — change her perspective on Tyrion and Sansa.
Even though Olenna had more of a motive than nearly anyone to kill Joffrey, by the look on Jaime's face during the third episode of Season 7, he had never considered her to be a true suspect in the death of his son. The same goes for Cersei, who so single-mindedly always believed that Tyrion had orchestrated Joffrey's poisoning. As evidenced by the fact that Jaime freed Tyrion after he was sentenced to death for killing Joffrey back in the Season 4 finale, Jaime obviously never believed his brother was responsible. So although he was horrified that it had been Olenna this whole time, there will eventually be part of him that is relieved to know for certain that it wasn't Tyrion and he'll report that to Cersei.
What Cersei will do with this news though is far less predictable. While she would probably never admit she was wrong in prosecuting Tyrion regardless, she's really not interested in making amends with Tyrion now that he's serving Daenerys Targaryen as her Hand of the Queen. Cersei also accused Tyrion's wife at the time — Sansa — of being involved in Joffrey's death, a belief she was still holding onto in the Season 7 premiere when Cersei called her a "murdering whore." So could the information that Olenna really poisoned Joffrey change Cersei's demented mind? When it comes to Sansa and Tyrion, Cersei always wanted a legitimate reason to hate them and as they are both currently traitors from her perspective anyway, don't expect her to deliver a mea culpa for blaming them.
Yet, there is something that could come from Olenna stating the truth — Cersei may sniff out the co-conspirators in Joffrey's death since Littlefinger and knight-turned-fool Dontos Hollard were the ones who helped the Tyrell matriarch in carrying out her plan. While Dontos was killed by Littlefinger in Season 4, Littlefinger is still very much alive and hanging out with Sansa. Cersei probably already wants to kill Petyr Baelish (who doesn't?), but if Olenna's reveal somehow leads to Cersei figuring out how involved Littlefinger was in Joffrey's death, she's probably going to take a more proactive approach in eliminating him.
While Littlefinger dying would be exciting for many Game Of Thrones fans, there was something particularly satisfying about the fan theory that a Stark would be the one to kill him. However, let's be real — besides Arya, the Starks aren't really known for murdering. Cersei, on the other hand, knows how to get the job done. So if you've been hoping that Littlefinger's manipulative reign will come to an end in Season 7, Olenna telling the truth about Joffrey's death could make that happen.
No matter how Cersei specifically reacts to the news about the death of her eldest child, it feels safe to assume that it will fuel her manic desire to hold onto the Iron Throne. Olenna betraying her back in Season 4 will prove to Cersei that enemies have been surrounding her on all sides. And though you would think that a person would find some solace in discovering that her brother had nothing to do with her son's murder, at the rate Cersei is going, it will probably only make her more power-crazed. So even with Olenna's confession, the odds of a joyous Lannister sibling reunion are just as grim as ever — just the reason for the hatred will be different.