Now that viewers are three episodes into the penultimate season of Game of Thrones, we're starting to get a sense of the breakneck, at best, and slapdash, at worst, pace we have to look forward to for the small handful of episodes we have left. Whereas it took Daenerys and Arya seasons and seasons just to find their way across the Narrow Sea and back to Westeros, Euron Greyjoy can apparently built a fleet overnight and apparate to any port he wants. Lately, he's been spending a lot of time in King's Landing, so will Jaime and Euron fight each other on Game of Thrones? Not necessarily.
Although Euron is practically begging for a fight, swooping into town to demand Cersei's hand in marriage in exchange for a fleet of ships, Jaime's conversation with Olenna right before killing her may have offered us some insight into just how exhausted with his sister Jaime really is. Euron has been taunting Jaime all season, knowing full well that he's in love with his own twin. He brazenly showboats (get it?) for Cersei in front of the Kingslayer, and he even whispers to Jaime that they should swap tips for how to ~please her~. Needless to say, Jaime seems like he's barely keeping his golden fist to himself.
But Cersei put a hold on Euron's proposal, saying their houses will only merge once the war is won. That seems OK with Euron for now, but he sure does look intent on wooing her. In Lady Olenna Tyrell's final conversation, she has a frank discussion with Jaime about his barbaric sister and her cruelties. She warned that Cersei will be his downfall, and he agreed that she may very well be right.
As Vulture pointed out, the prophecy that predicted Cersei's three children would die also contained information about the queen herself. It foretold that her little brother "shall wrap his hands about your pale white throat and choke the life from you." Most book readers assume this prophecy refers to Tyrion, given his well-documented hatred of Cersei and her animosity toward him. But she is technically the older twin, so she does have another little brother. What if Jaime finally comes to his senses and realizes that Cersei is totally unhinged, no longer the woman he loves, and no longer a mother to his now-dead children. He's slain a mad king once before — who's to say he won't slay a mad queen?
Euron and Jaime's rivalry is obvious, and it may indeed come down to fisticuffs between them. But Cersei and Jaime's potential conflict is a much more serious looking one.