One major theory that seems to have caught a lot of traction is that Jamie is the new hero beyond the wall Azor Ahai. The connection made is the story about how Azor Ahai forged his sword,
" Darkness lay over the world and Azor Ahai was the hero chosen to fight against it. To fight the darkness, Azor Ahai needed to forge a hero's sword. He labored for thirty days and thirty nights until it was done. However, when he went to temper it in water, the sword broke. He was not one to give up easily, so he started over.The second time he took fifty days and fifty nights to make the sword, even better than the first. To temper it this time, he captured a lion and drove the sword into its heart, but once more the steel shattered.The third time, with a heavy heart, for he knew beforehand what he must do to finish the blade, he worked for a hundred days and nights until it was finished. This time, he called for his wife, Nissa Nissa, and asked her to bare her breast. He drove his sword into her living heart, her soul combining with the steel of the sword, creating Lightbringer. "
In connecting it to Jamie, they say that the forging of the sword is a metaphor for forging ones character (persona not backstory). The wide spread theory for now is as follows. Using the first time Azor quenched his sword in water. As for how that connects to Jamie, its the scene of him in the bath house with Brienne of Tarth. He came clean about killing the mad king, and afterwords gave into his exhaustion which you could call a "broken man". The second attempt of making a sword he plunged it into the heart of a lion. Very similar to how Jamie broke the news to his brother Tyrion while he awaited trial for the death of Joffery. Thus shatter the heart of a captured "lion".
He's my twist which seems like something that George R.R. Martin would do. Many seem to jump straight into thinking he's going to fulfill the prophecy by killing Cersei. Which would be the last part, him killing her and becoming the hero. Sure I do not disagree he will become the hero, but it won't be Cersei. He is going to end up killing Brienne, as for why or how I'm not positive. But its been seen how she looks at him and how much Jamie has come to resent Cersei so how could she be his love.
If you liked my twist on this theory, drop an upvote, leave a comment if you think I'm possibly right.
Thanks for reading.
~Tex