The diclonius (two-horned human) was a mutant created by humans. It had a special ability that could be described as a sixth sense.
The mutants had enough power to exterminate the whole human race. Humans being afraid of their powers, they were isolated into research labs to be studied.
One of the diclonius girls named Lucy broke out of confinement, killed the guards and escaped from the laboratory. She fell into the ocean after being shot and ended up on a beach. There she met Kota and Yuka, they named her Nyu and began to live with her.
This episode takes place within episode 11 as Nana attempts to fit in the household while trying to find a chore that she can do and get used to Nyu's presence whom she only knows as Lucy. Running away after getting scolded, Nana ends up in the beach and meets Bantou whom she promised to bring Lucy to later that night. Leaving the household with Nyu, it begins to rain and Nyu slips, hits her head, and is knocked unconscious. As Bantou waits and everyone else worries where they might be, Nana, with an uncoscious Nyu, takes shelter as Lucy's consciousness begins to come out and dreams an old memory of how she was captured and why she doesn't attack Director Kurama. As the rain begins to let up, Kouta and the others find Nana and Lucy and takes them home. There, Nana finally finds the chore that she will be doing - feeding the dog.
Occurs during the events of Elfen Lied TV episode 11; considered as "episode 14."
an extended description!