Lightbringer (Book Spoilers)
After having watched the episode I have no idea who Azor Ahai is supposed to be in the show. Perhaps AA is just an amalgamation of all our heroes since many of them made necessary contributions. However, I'm pretty sure I recognized AA's legendary weapon.
Melisandre = Lightbringer.
Twice she illuminated the battlefield by setting the Dothraki's swords and the moat on fire. You could say that she gave Arya a moment of enlightenment by reminding her that she would shut "blue eyes".
The episode also brought to mind the legend of Lightbringer,
Darkness lay over the world and a hero, Azor Ahai, was 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 before hand 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 breast, her soul combining with the steel of the sword, creating Lightbringer, while her cry of anguish and ecstasy left a crack across the face of the moon.
There's a lot going on here. The three attempts could represent multiple characters or events. Maybe we're supposed to see Mel's personal search for AA in Stanis, then Jon, and perhaps finally Arya. It could also be the three battles we associate with her: the battle of Blackwater Bay, Stanis' last stand at Winterfell, and the Battle for the Dawn 2.0. Stanis' ships are literally broken and shattered by wildfire in Blackwater Bay. Lions are a traditional symbol of royalty. The second tempering could relate to the sacrifice of Shireen or the execution of Stanis that happened around the battle with Ramsey. The third battle is maybe the hardest to relate to the myth. Is there a sacrifice in the episode comparable to Nissa Nissa's? I think part of the answer will be found in the future books, but perhaps Mel herself, at least a part of her, is that sacrifice. The OG Lord of Light once said, "The meek shall inherit the earth." When we meet Melisandre she is arrogant, prideful and merciless. She returns as a humble servant of the Lord, and is ready to lay her life down once her purpose had been fulfilled. No one is going to forgive her for what she's done, but I like to think she's sacrificed a part of herself on the road to atonement.