Aiko Takada was the second human to befriend Lucy. She made her only appearance in Chapter 85 of the manga series and in the special OVA episode of the anime, both of which are almost exclusively devoted to her backstory.
Though she only appears in one chapter/episode, Aiko's impact on Lucy is as vital to her character as Kouta's. Lucy wished to help Aiko reunite with her mother, and it's through Aiko's kindness toward her that Lucy began to humor the idea that she could be more than just the murderer her DNA Voice said she was meant to be. It is Aiko's death that ignites Lucy's vendetta against Kurama, a vital component to Elfen Lied's plot.
Five years after murdering Kouta's family, Lucy is on the run, killing some humans and infecting others with the Diclonius Virus in the Kamakura area, as many as two hundred. Lucy accomplishes these murders by using her vectors on people's blood vessels to simulate heart attacks. After being accidentally hit by a kid's soccer ball, an offer of aid from Aiko, which she, at first, reluctantly takes, ends a potential rampage.
Aiko then asks her to be a model for her drawings, revealing that she had already sketched her in the park from her apartment window. Her artwork, however, aroused the ire of her father, who greatly resented her mother (who was also an artist) for abandoning them. Aiko's father beat her in front of Lucy, who tossed him around with her vectors. She spared his life only to spare Aiko's feelings. Aiko tells her that she still dreams of her family being united again, despite never actually having known her mother. She reveals that her mother, now a famous artist, is likely in the area with a showcase of her works at a local mall. With memories of her regrets about Kouta still haunting her, Lucy strongly urges her to go and see her mother, no matter her fears and anger. They resolve to go and see her the very next day, at which time Aiko will give her a gift, a painting she made and hid away. Unbeknownst to her, her mother in fact desired to see her very much.
Following a grim premonition, Lucy went back to Aiko's apartment. When she arrived, she found that Aiko had accidentally killed her father. Having seen a painting she made for her mother, he tried to slash it with a knife, only for her to push him away from the painting to save it. This frenzy led to him cutting his throat. Lucy told Aiko it was, in fact, her fault, since the hidden picture was exposed when she threw Aiko's father. They planned to go to the police the next day, but the arrival of the father's barfly girlfriend, who openly and loudly accuses them both of murder, ends that. Promising that Aiko will meet her mother, Lucy gets her to agree to go on the run. The instances of massive amounts of heart attacks and Diclonius births caught the attention of Diclonius researchers Kurama and Kakuzawa, who reach the conclusion that perhaps the original Diclonius is in the Kamakura area. Their search narrows with the report of Aiko's father's murder and when they find an old photo of Lucy and a statement that she was the only child missing after the murders she committed five years before. Lucy and Aiko broke into the mall where her mother had the art exhibition, hoping to meet her. Aiko is briefly heartened to see a painting of her as a baby with her mother. Outside, Kurama leads the team that will try to go in and get Lucy. Inside, Lucy uses her powers to amuse Aiko and convinces her that she is a magician, but is put off by Aiko's talk of a hopeful future together. Surrounded by the armed guards led by Kurama, who at first urges restraint, a panicked Lucy begins using her powers. Attempting to protect Lucy, Aiko is shot by Kurama. Enraged, Lucy kills many of the guards. In the distance, Aiko's mother, who was one of the guests cleared out before the assault, wondered at the carnage. To try and save her dying friend, Lucy surrenders.
Once in captivity at the Diclonius Research Institute, she is informed by Kurama that Aiko has died. Kurama states that it was her fault for not surrendering, just as Diclonii 'deserve' their treatment for not wanting to co-exist. Infuriated, Lucy vows to kill off the people Kurama loves but to leave him alive to suffer the pain of losing someone he cares about so he'll suffer the way he's made her suffer.
Dead, or Alive?
In the final chapter of the manga, Wanta can be seen passing a poster that appears to be advertising an art show for an artist named "Takada Aiko," throwing suspicion on whether or not Aiko indeed died that day. While no official word clarifies what happened, there are several arguments for and against her survival that depend on circumstantial evidence.
The poster's characters translate to "Takada Aiko, Artist" and detail an exhibit of hers taking place at a local department store. Unless her mother's name is also Aiko Takada, it is unlikely the exhibit is on her mother's show.
It is possible the Institute offered an injured Aiko the chance to have the accidental killing of her father covered up by the facility (as in Japan she would be imprisoned for murder instead of manslaughter). In exchange for forgetting about the incident entirely, she might have been allowed to reunite with her mother.
Kurama may have thought that to tell Lucy the girl died would remove any reason for her to escape the facility to try and rejoin her.
Since amnesia is common in Elfen Lied, it is possible Aiko was so traumatized by the events that she forgot who Lucy was, or she was medically induced to forget it in the hospital under Kurama or Kakuzawa's orders.
Kurama had no reason to lie to Lucy unless out of sheer malice. For all Kurama knew, knowing the girl survived would have made Lucy honor her promise and stay within their hands.
Aiko staying alive would have led to her being always watched by agents of Kakuzawa, if not resulted in her death from Chief Kakuzawa's paranoia.
If Aiko died, her few possessions would likely go to her mother, including her drawings. The indicated show could have been in her honor, and the picture seen a photo altered to show what a grown-up Aiko would have looked.
The bullet that injured Aiko went clear through her chest, and she immediately ceased motion whereas most people would go into shock from the pain and even seize. This evidence makes it highly likely she died instantly. However, this is only the case in the anime, as the manga shows her fully conscious and speaking until being carried away.
In the manga, Aiko coughs up blood after being shot, meaning the bullet went through the lung, and her lungs are beginning to fill with blood. Being shot in the lung makes it very likely she could die of her lung collapsing or from drowning in her blood unless receiving immediate medical attention. If the bullet hit the heart or a major blood vessel in the area, she would still die from bleeding out without immediate medical care.
Aiko's demeanor toward Lucy suggests she had a crush on her, as she would often draw her and appeared flustered around her. The hints are stronger in the OVA, where Aiko even kisses her cheek and says she likes her (using "suki," which is commonly by teens confessing their feelings to another).
In many mass media interpretations of comic-based works, the hero's great secrets, normally sacrosanct and protected by the writers ad absurdium, are often treated more loosely and sometimes not as a concern at all. In that light, the fact that Lucy reveals her horns to Aiko in the anime can be seen as part of a trend.