I want to go in a different direction and talk about the significance of this DLC, what it actually does explain, and some theories that are created from this chapter.
--The chapter starts off with Lightning and Caius locked in combat, while Serah and Noel proceed though Academia 500's maze. There's no telling how long they were fighting, as there's no time in Valhalla, but it shows they are evenly matched. In a fight that could last an eternity, Caius uses a vision of Serah to give himself an advantage. It's a vision of what's to come, Serah's death at the Eyes of Etro, and he is able to use this through his knowledge of the entire timeline, allowing him to beat Lightning by throwing her off guard. As he walks forward to deliver the finishing blow, a flow of chaos surrounds Lightning and whisks her away.
I believe this chaos to be the Yeul, the one that exist in all the ages. Let's call her Chaos-Yeul.
--Lightning awakes at Etro's throne as the chaos she was previously engulfed in forms in front of her. At this point, the chaos is voiced by Yeul, and she shows Lightning a Serah trapped in chaos. She then, taunts Lightning, explaining to her that Serah is in the hands of chaos and that she will never be released. The chaos surrounding the area begins to focus at Etro's throne as Chaos-Yeul attempts to claim Lightning as well, laughing at her helplessness. Lightning draws her sword, once again locked in combat against a Caius formed by chaos.
The Caius you fight in this DLC is not the real Caius, just chaos taking the form of Caius, like in Vile Peaks with Twilight Odin. The difference is, Yeul is shown to be behind this fight, keeping Lightning occupied while the real Caius stops Serah and Noel in Academia. This is the very same Yeul who tells Serah and Noel not to fight Caius, stalling them with Amethyst and Luvulite, the crystalspawn born from chaos. While she does tell them what will happen if they proceed to kill Caius, which is what Chaos-Yeul and Caius want, she easily manipulates them, giving them the strength to see it through to the end and even provides the path for them. The pillars moving in Academia are controlled by chaos...
--Lightning defeats the chaos formed Caius and proceeds to return to where the fight had originated earlier. While riding on Odin, she once again confronts the wandering chaos, telling it to "Let my sister go". The chaos forms into a Yeul silhouhette, responding "By what right to you demand her release". Before Lightning can answer, she is surrounded by chaos and begins to sink into it, like quicksand, along with Odin. Chaos-Yuel reminds her that Serah's death is her doing as Lightning is finally consumed by chaos.
Chaos-Yeul is shown consuming Lightning into chaos, something she wasn't able to do when she approached her earlier. At this point of the DLC, Noel had already killed the Goddess by stabbing Caius, allowing chaos to run free, and Serah had already died in Noel's arms. So Chaos-Yeul being able to consume Lightning at this point but not earlier makes sense. What she did not expect was for the two consumed sisters to meet, and through a touching conversation, Lightning is able to break free of chaos' grip, returning to Etro's throne. During their conversation however, Serah was further sacrificed to bring Lightning back to Valhalla, it was a one time deal. There would be no way for Lightning to break free from chaos again should she be consumed, and the world is on the brink of such a fate. The crystal tear that Serah shed, which she also shed in XIII, would give her the idea of turning to crystal so that chaos couldn't get to her. By turning herself to crystal, atop a very recognizable place, she could preserve her strength for the time when someone or something finds a way to stop chaos from roaming free.