The depth of the general story of Elfen Lied is that of racism, ostracization, bullying, ethnic purification, bullying, segregation and domination that has been seen present in humanity since the dawn of time.
"In persecuting those we view as 'inhuman', we thusly become less human than those we persecute". That is the message behind Elfen Lied.
The Nazi Party viewed Jews as sub-human. They ended up committing one of the most revolting inhuman acts in history. The American settlers viewed Native Americans as sub-human. Their slaughter is a scar on the face of history.
Elfen Lied just replaces Jews and Native Americans with Diclonus, and scales their numbers down to individuals rather than entire races as the examples above.
Elfen Lied also presents conflicting visions of good and evil in nearly every facet of human life, showing its opposite extremes.
Science can be used for beneficial purposes such as curing diseases, or it can be used to torture little kids with cruel experimentation in the name progress. Sex can be an expression of love between two individuals coming together, or it can be perverted and used by a pedophile to victimize a child. Lethal weapons (be it guns or Diclonus-arms) and warfare can be used to protect the innocent and save loved ones or murder the innocent and take loved ones away.
All are illustrated in Elfen Lied.
Lucy herself was an example of evil and innocence living in the same body. A monster of bloodlust crafted by the uncaring world around her, and an embodiment of her own lost innocence, both guided to the enlightenment of human emotion through friendship with those around her, eventually becoming truly human in both cognizance and definition, more so than the people in the organization who sought to capture, control, exploit or destroy her.