elfen lied - Who was this girl by Lucy in special episode 10.5

In special episode 10.5 of Elfen Lied anime, there was a scene where Lucy was together with a girl in a school. Who was that girl? A friend? And why did she want to protect her? I thought Lucy hate

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Erufen Rīto, a.k.a. Elfen Lied, OVA special, episode 10.5, Tōriame ni te arui wa, shōjo wa ikani shi te sono shinjō ni itatta ka? a.k.a. In the Passing …

Elfen Lied Anime Transcript - Episode 14/OVA/10.5, Elfen Lied Wiki