Lucifer and Alexial? Lol, it's an obvious guess. xD
In order for anything I say to make sense, you'd have to know the history about Alexial and her imprisonment.
Alexial was imprisoned within Eden for a long time, due to God's determination to keep her away from her brother, Rociel. She met Lucifer when she wanted to escape the prison she was in. But when helping her escape, he was taken captive by God and sentenced to be imprisoned within the Nanatsusaya*.
At the time, it was when Alexial decided to rebel against Heaven. In which she did but was captured and sentenced to imprisonment within Eden's cage and her soul to be sent to Earth to be reincarnated repeatedly as a human, dying gruesome deaths whenever killed. (an example would be... well, let's say bloody 'accidents')
Lucifer's spirit, however, searched for her so he reincarnated as someone close to the reincarnated life she lived everytime and kill her himself so she won't die a gruesome death by her punishment.
It's kinda obvious that he liked her and it was because of a promise he made with her a long time ago, as so it is mentioned in Volume 20. And she liked him back since he helped her anyway. But she also liked her own brother Rociel. ^_^"
And the rest is history. >_> Sorry if none of this makes sense. Lol