It should be clear by now that nobody is ever really safe on Game of Thrones, and as the story begins to wind down, it's all but guaranteed that some fan-favorite characters are about to bite the dust. So could Jaime die on Game of Thrones? I think he's probably fine for now, but there is a solid chance I am wrong.
In the fourth episode of Season 7, Jaime's forces and supplies were being roasted alive by Daenerys and her dragon, so Jaime decided to do the gallant and stupid thing by charging at Dany and Drogon with a spear to try and stop them. This did not go well. Drogon immediately turned to breathe fire at him, protecting himself and his mama. Jaime was not immediately burned to a crisp because Bronn swooped in and shoved Jaime out of the way, plunging them both into the very conveniently located lake. The last lingering shot of the episode showed Jaime floating away, weighed down by his heavy Lannister armor. I don't think that this is really the last of Jaime Lannister, but I've been wrong before. There have even been hints that Jaime isn't going to be around much longer, and he may not even see the final season.
One of the images released for Episode 5 shows Cersei seated on a large bed (see above), staring pensively into the distance. This is the bed where we last saw Cersei and Jaime lounging in post-coital bliss, which seems to indicate that Cersei is thinking about Jaime in this picture. Has he been reported dead? It would make sense for Cersei to look this troubled if she had received word that her beloved brother drowned in Blackwater Rush. There's not much that makes Cersei seem human anymore these days, but her brother is one of the few things that actually does.
On the other hand, perhaps Jaime is not dead, and Cersei has just learned that Olenna Tyrell killed Joffrey and not Tyrion like she thought. This would also be some information that would probably make Cersei feel she needed to sit down to fully process. In an interview with The New York Times, actor Nikolaj Coster-Waldau who plays Jaime notes that the character was luckily not wearing his brass Kingsguard armor when he fell into the water. "It seems impossible to survive that," he said, which I'm choosing to interpret as hard evidence that Jaime isn't going anywhere yet.