The images of Lucy and Nyu remind Kouta of his long-ago promise that, if someday she ever started killing lots of people, then Kouta would have to kill her. The inner voice tries to object but is over-ridden. While they don't wish to die, they know lots of people will die so long as she is alive, and they cannot cause the body's death by themselves, so they urge him to kill them.
As their essences fade again, Kouta sees his childhood friend on the beach, as she tells him that she knows she can no longer live with the others at the Maple House and that she must die for the thousands she has killed. She says that she can die without regrets if he is the one who kills her, but Kouta refuses, saying he would miss her if she were gone. She reminds him of the place where they first met, near a large stone, and says that he should come there on the last day of the summer festival. She will always be waiting for him there, and if she is reborn, she will be a good girl, and how wonderful it might be to be by his side forever.
Illusionaryprotection
That's not how DNA works, but at this point in this story in particular, it's silly to point such things out.
The spirits of Lucy/Nyu fade away for good, urging him to kill her quickly since they can no longer stop the attacks by the DNA Voice personality. Kouta picks up a gun, apologizes and prepares to shoot as the voice curses him. But at the last moment, he drops the gun, still seeing the hateful monstrosity as his dear friend. It seems inevitable the unlimited, pain-driven voice will kill them all now as well as the world, starting with Kouta. Nana cries out, and then all settles down.
The voice, perhaps moved by his initial inability to shoot and overwhelmed by the pain it can no longer bear, puts the gun back in Kouta's hands, pleading and begging for him to end its pain once and for all. In tears and grief with all his friends and loved ones watching, he shoots and kills the girl known as both Lucy and Nyu.