Lucifer, also known as Satan, the Devil, and Old Reg, is a Lord of Law, and the first being to rebel against the Balance. Lucifer, in his aspect as Old Reg, is the supreme dictator of the Singularity, and commands the full power of Law's Straight-Arrow fleets.
On other levels of reality, the Fallen Angel has a very close relationship with the Von Bek family. They are sworn to seek the Holy Grail to help Lucifer cure the World's Pain and reconcile himself with God.
It is very possible that Lucifer is somehow one with the Black Sword, as he himself has stated.