So... is Elfen Lied finished or not?
It is a bit ambiguous in this case.
Why?
The anime finished before the manga:
Anime finished: October 17, 2004
Manga finished: August 25, 2005
We could not confirm the source content in MangaUpdates.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Elfen Lied tells the story of Lucy, a Diclonius with powerful telekinetic abilities, who escapes from a secret research facility. This escape is bloody and violent.
During her escape, a head injury causes her to develop a second, innocent personality. She is found by Kouta and Yuka, two college students who take her in.
Unaware of Lucy's dangerous past and the powers she possesses, Kouta and Yuka's lives become entangled with the government's pursuit of Lucy, leading them into a world of secrets and conspiracies.