Lucifer is a Roman word meaning Light Bearer.
Many say that this was used to refer to a Pagan God that the christians saw as a Devil and was also associated with Satan by them. Some would agree with the greater Key of Soloman translated by Mathers that it is a false name of the demon Lucifuge and sits in the House of Binah, but Lucifer actually was the name of the leader of a group og Angels who were called "The Brilliant Ones" and rested in the House of Binah on the Quabalistic Tree of Life, the next highest seat to Kether which upon this tree represents the House of God.
After the Fall from the group this leader kept to himself the name of Lucifer to signify him as the bringer of false light.The Angels from the group called the Brilliant Ones who fell with Lucifer was after the fall then called Lucifuge and what a better name for the Angel's who fell with him from his own group.
The way in which we know that the name Lucifuge is a group name and not a name for a single entity is by reading the Grand Grimoire which calls on Lucifuge Rofocale to make a pact and he is called in the name of Lucifer. As a matter of fact Lucifer is asked to send Lucifuge Rofocale to the Magickian.
Another way we can see that this name refers to a group and not a single entity is to read the fourth book of Cornelius Agrippa, which is actually another translation of the Greater Key of Solomon, but much older than the one by Mathers.
In this older translation it states that Satariel is the leader of the Lucifuge.Mathers translation statesthat Lucifuge is the leader of a group of Demons called the Satariel.Mathers calls them the cowardly ones, but judging by the sources you can plainly see that Lucifugeis a name refering to a group not a single entity.
Many people say that Lucifuge Rofocaleis actually another name for the Demon Focalor, and I would say this is very possible since he bears the same traits, but if you will notice in the Grand Grimoire that he adds the name Lucifuge before his name, signifying his titleas one in Lucifers service.
In other books that speak of Focalor he was well loved by Lucifer and another way to see that Lucifer is a legitimate name of the leader of this group is by reading the Lesser Key of Solomon(Goetia) also translated by Mathers and originally a part of the Greater Key of Solomon together the were called the Clavicle of Solomon.
In the section where Solomon talks about what Belial can do for the Magickian, Solomon states that Belial will tell the Magickian that he was first to fall after, not Lucifuge but Lucifer and also if you read where he talks about other Demons mentioned and called upon in the book you will come to Paimon whom it states is well loved by Lucifer, not Lucifuge. The evidence speaks for itself.

You can obtain copies of these booksas special orders from Borders, they often stock the Greater Key of Solomon by Mathers and the fragment of the Grand Grimoire which speaks and calls on Lucifuge.Rofocale can be found in the book "Pacts with the Devil"written by Christopher S. Hyatt & S. Jason Black.

The opinions written above belong to Rev. Michael Cardinell if you would like to discuss any of these ideas and/or statements please feel free to e-mail me and we can discuss them.Also read the books mentioned above to form your own opinions.

It is also my opinion that we must always examine all the evidence we have on Satan, Lucifer, and the Lucifuge and not take the word of just the christian bible, if you do this you are missing out on alot of knowledge and beautiful histories of these entities thatmost associate as being one.