This was very good, and the song did fit the show. The theme of the show wasn't just violence, but it was also sort of a psychological drama/horror
The song is depressing, but beautiful and represented Lucy's childhood. When Lucy heard the song it reminded her of the time she had fun with Kohta (Think I'm spelling it right)
And the opening theme also kinda made it look like all she had was herself and her inner being her whole life. The opening and song was perfect for the show.