If you've watched the epic final battle scene in Game Of Thrones Season 7 Episode 4, you'll know that someone (probably Bronn) knocks Jaime into the water when Drogon unleashes a jet of flame directly at him. But does Jaime drown on Game Of Thrones? The fact that Jaime seems to sink further and further into the water (rather than struggling to get out of his armor and stay afloat) was troubling, as was the fact that the episode closed on the image of Jaime sinking into the darkness. Besides, the beauty of the series has always been its willingness to let major characters suddenly, unexpectedly meet their makers (see: Ned Stark, Robb Stark, Margaery Tyrell, heck, even theoretically Jon Snow, who did physically die even if he came back).
So far, we haven't had a really major death in Season 7. As such, if the Kingslayer died in as mundane way as drowning thanks to the weight of his armor (rather than in the heat of battle), it would hammer home how high the stakes are and the fact that absolutely anyone in the show, regardless of how central they are to its narrative, can bite the dust at any time.
On top of that, there was no sign of Jaime in the preview for Game Of Thrones Season 7 Episode 5. While you could argue this is to avoid undermining the cliffhanger (if it's just that and not a death), the scene showing Daenerys ordering Jaime's soldiers to bend the knee hinted that the Lannister twin could really be gone for good. After all, as the battle scene proved, he's not one to abandon his troops when the going gets tough. It hardly seems likely that he's simply surfaced upstream and run away.
Tyrion's presence for the battle also seemed to be in favor of an actual death. By positioning the Hand of the Queen on the sidelines shouting at his brother to get out of the way, it reminded us that Jaime isn't just vital to the story for his military expertise but because of his familial bonds. Tyrion's reaction reinforced how complicated the war could get if any of his family are killed by his boss. Given that Thrones delights in lingering in these gray areas of morality and that this season seems to be all about how a just ruler should behave, Jaime's death would open up new territory in terms of Tyrion and Dany's relationship.
And let's not forget his hand. Jaime isn't just weighted down by some incredibly heavy looking armor (complete with decorative metal lions on the shoulders), but a solid gold hand, which would make it extra hard to swim to the surface.
All the same, the plotting of the episode seemed to suggest that he wouldn't actually drown. After all, why have Jaime saved from a jet of flame at the very last minute if the showrunners were just going to let him drown? Surely if they'd been intending for him to die in the battle, having him toasted to a crisp by Drogon would have been a suitably dramatic way for him to meet his end, as well as embodying all of Jaime's faults in one brief moment. Namely, stubbornly insisting on fighting his sister's cause even when all odds seem to be stacked against them; his reliance on brute strength rather than smarts; and his emphasis on honor and the code of battle and refusing to simply run away, as Bronn advises him to.
So, it seems unlikely Jaime will actually drown; that ending was far too ambiguous. Every major character death so far has been deeply explicit. Think Joffrey going purple and clutching at his throat; Ned Stark's head on a spike; Robb Stark getting shot by multiple musicians with crossbows. The joy of this final season is that there is no right team to root for. Jon Snow's focus on fighting the White Walkers and Dany's insistence on justice and sparing civilian lives both make them strong contenders for audience favorite. Minus the sympathy Jaime brings to her team, Cersei becomes the default baddie. And Thrones doesn't work like that, with clear boundaries between good and evil. Jaime is probably just fine.