It seems most likely that it is Justice. Unless it is another sword that has not been mentioned to the readers yet and Rand will mention it's origin later. Maybe he read about it in a book. But that seems less likely. If it is one of Gaidal Cain's swords then why is there only one? But it would definitely have to be one that Rand has either learned about or possibly saw at Falme. He said that it was from his memories and not LTT's.