Well, it feels more like what Elfen Lied would have been if set in a medieval setting. A vengeful amnesiac that lost her memory, with a strong desire to kill her captors. It's the amnesia aspect that makes it sing Elfen Lied, not your avatar. That in combination with "Intelligent, manipulative, morbid and most of all, broken." and "She lives her life by deceiving and using others ruthlessly, only caring for herself." enhances the feel of what Elfen Lied was.
Because that's what Lucy did, before she fell in love with one of the main characters that she eventually sacrificed her life to protect.
Now, your backstory may be long. But it actually doesn't say all that much.
Her origin is shrouded in mystery thanks to the amnesia, They do explain how she gained/regained her two imbued swords however. But no one goes from losing everything to becoming a torturer unless she already was twisted.
The story, summarized, is about a woman who escaped a research facility as a amnesiac, breaking out and looting herself two useful swords and having a man she recently met that brightened up her day result in her world being darkened further. On a related note. I thought your character had such a emo tone to it, that is why I created such a happy character. ;D