The double murder of Kouta's sister Kanae and their father by Lucy's hands speak volumes of her descent into madness, despair, and hatred. Unlike the deaths of thechildren in the orphanage and the first murders of the festival-goers preceding the train murders, these killings were not spur-of-the-moment crimes of passion brought on by unspeakable despair. Although Lucy found herself overcome by her emotions and the feelings of betrayal, the murders of Kanae and her father were calculated, premeditated, and acted out in a warped sense of cold-blooded payback.
Lucy bid her time well. Rather than attack at the station as Kouta, his father, and Kanae said goodbye to Yuka and her mother for what they assumed was only another year, she waited and watched. Rather than kill Yuka and her mother after Kouta and his family boarded the train, Lucy snuck onboard the train herself and waited in the next cabin. Only after Kanae's fight with her brother did she finally make her presence known, and while Kouta was happily surprised to see her, Kanae feared for their lives from the moment she saw her. Her pleas for her brother to run away fell on deaf ears, as Kouta refused to believe his friend could be responsible for the deaths at the festival. As Kouta told his sister he hated her for lying to him; Lucy killed the girl by cutting her in half at the waist. As Kouta screamed and his father cradled the brutally maimed corpse of his child, Lucy merely laughed, saying Kouta was the stupid one and not his sister. When his father turned his attention toward her, perhaps meaning to scream at her, she killed him instantly by beheading him. In shock, Kouta asked her why she would do this to him. After all, weren't they friends? The girl's answer was that they were friends, and their friendship was the only reason Kouta still lived. As Lucy walked past him, she stated Yuka would be her next prey, prompting Kouta to tackle her, shake her, and beg her to stop. As he pleaded with her to cease her bloodshed, Lucy wondered how it came to this. She knew that all she'd wanted was Kouta's affection, yet she'd caused him so much heartbreak. She tore a hole in the roof of the train to escape, leaving Kouta alone with the corpses of his family.
Lucy proves through these murders that she is every bit the slave to her emotions that all children tend to be. Children, like adults, possess logic and reasoning, but due to their lack of experience, such logic and reasoning tends to revolve around themselves. Rather than consider what is right or wrong from an altruistic standpoint, they believe what is right to be based on their wishes and whether or not the actions done to them hurt them or help them. In spite of her upbringing, or lack thereof, teaching her to guard her emotions so they won't be abused by others, she easily gives in to callous vengeance over a white lie. On the bus ride home, she wonders what she would do if Kouta's cousin was indeed a girl. If he wouldn't go to the festival with her but with another girl instead, her feelings would be hurt, and to a child's mind, the best way to handle being hurt? Often, it is to hurt the one who caused it. The DNA Voice exacerbated the situation by suggesting it was the right thing to do, and Lucy was already so far gone into what it suggested that she attempted to strangle Kouta for the slight he hadn't yet committed before she realized what she was doing. Immediately after the murders, her coldness toward Kouta as he grieves and asks her why she killed his father and sister is that of a child scorned. He's ignored her feelings by lying to her, but now she'll make him suffer for it. And what better way to make him suffer more than to go and kill the girl he lied about in the first place? It would also free her of her ties to the world. Without Kouta or his family in her way, she could go about creating a place for herself where she wouldn't ever be hurt by other people again, where she would be surrounded with people like her who cared about her and wouldn't treat her as badly as those she's met thus far.
Like many young Diclonii, Lucy had no idea of the full scope of her powers when they first developed, nor did she grasp the consequences of using such power. She first used them in a moment of passion, killing the children who not only bullied her but murdered her pet. After that, she used them to kill others so she could use their homes as shelters, and she did so without truly grasping the severity of what it meant. It was just a means to food and a warm bed at night, things she couldn't have since she was on the run for the mayhem in the orphanage. The idea that what she was doing was wrong came to her during the trip with Kouta to the zoo, but it was swiftly forgotten as the two had a fun and carefree day Lucy herself never got to experience before. This realization didn't come up again until after the murders when she realized too late that, in seeking to make Kouta pay for lying to her, she ruined his life completely. Other Diclonii likely reached similar epiphanies after killing their own families by accident; those they killed with their amazing powers wouldn't come back, even if they didn't mean to hurt them.
The murders of Kouta's family members are examples of how far Lucy fell into her destructive feelings, as well as the tipping point for her becoming a mass murderer. They are the sign to Lucy that her choices and her actions have weight, as well as signs that she is not always in the right, but at the same time, she concludes from them that being a killer is just what she was born to do. After the murders, she takes to Kamakura's streets and continues to kill people, either to infect them with the Diclonius Virus, to take their homes for a few nights, or simply killing them just for the sake of it. While mourning her actions against Kouta, she does nothing to actively stop them when geared toward other people. Once more, killing becomes a way to have food and a place to sleep that isn't the streets, with only the occasional lament that she's fallen into the pit of killing in cold blood.
The murders also lead her to be more careful when she meets another friend in the future, and a possible chance at redeeming herself and proving she isn't solely a heartless killer. However, despite her efforts to do right by her new friend and try to correct herself, things do not go as she plans. The murders also lead to her arc of atonement in Elfen Lied's main plot in both the manga and anime, as Lucy's reasons for living are vengeance for Aiko and apologizing to Kouta for what she's done.
Why? Why has it become like this?
–Young Lucy, only beginning to realize the cost of what she has done