Let it be known that because of GRRM's take on prophecies, there is flexibility in interpretation.
Lightbringer, a fiery red sword. The theme among the entire series is, of course, Ice and Fire. Ice is Ned Stark's Valyrian steel sword and is the first cover of the first book of the A Song of Ice and Fire series: Game of Thrones. I also think that Gendry is going to be the one who reforges it. More on that later.
King Joffrey's first sword was thrown into a river by Arya Stark.
Second sword Joffrey had lost was named Hearteater. It was lost at the Battle of Blackwater, the same battle Tyrion had almost lost his life to Ser Mandon Moore.
In ASoS, Tyrion said of Mandon Moore:
Tyrion's description of Widow's Wail:
Continuing the Lightbringer prophecy:
Now, in ACoK it is revealed that Ser Ilyn Payne never washed Ned Stark's blood off of Ice. Ice was then broken down into two swords: Widow's wail for Joffrey and Oathkeeper for Jaime. Widow's wail fits appropriately because of Catelyn Stark's morning for Ned Stark's death and the shattering of her family. It also fits Cersei as well, but that is for another post. Oathkeeper was given to Brienne of Tarthe. I think all the alive Stark siblings will get together again sometime in the books, thus fulfilling Brienne of Tarth's oath to Catelyn.
I said that Gendry would be the one to reforge the two swords into Light Bringer. His last whereabouts was rowing to King's Landing, the location of metal worker who was able to temper Ice down the two swords is. (Or maybe, after killing Cersei, that is when they will remake the sword). In the first chapter in ACoK, after the comet prologue, Gendry comments how the comment looks like a Red Sword. Later in ACoK, Catelyn is praying to the seven and when she turns to the Smith, her description of it is:
One who fixes things that were broken. The Stark family. Oathkeeper and Widow's Wail. Though, the reason why I draw this conclusion from this passage is because Catelyn describes the Stranger in a way that resembles Arya as well as Cersei and the Mother.
The person who melted Ice down into Oathkeeper and Widow's Wail is Gendry's master. The last time we see Gendry in the TV series, he is heading back to King's Landing. I don't know what happened in the books, but Gendry or his master will be the one to reforge the two Valyrian swords, Oathkeeper and Widow's Wail, back into Lightbringer after Brienne has brought the Stark sibblings back together. In Jaime's dream:
Both swords are aflame. Meaning that it will become Lightbringer.