The theme of sci-fiction comes into play in both series.
Additionally, there are characters that are unique in t heir own ways and hints of romance (less so in No. 6 but based on mutual respect/affection).
Both series also has drama and small bits of comedy.
Opening theme contains paintings by Gustav Klimt.
The main character - Ray, like Lucy, suffers from multiple personality disorder, does not know anything about themselves and their parents. Ray - a wonderful surgeon, thanks to his extraordinary abilities. Lucy could also be an excellent surgeon, as vectors can do extraordinary things.
In the anime, there is a man who tortures people for their own experiments, as the benefits, like Director Kakuzawa in the Elfen Lied.