The name "Lucifer" appears only once in the Bible, in Isaiah (KJV), where he alludes to the tale (which we can assume is already known to his Jewish audience at that time) of the great Lucifer having fallen from heaven, being cast down and looked upon with contempt, in order to draw a parallel to the king of Babylon and his kingdom's impending fall.
Lucifer means "morning star", which is used various times and in various ways in the Bible, including by Christ to refer to himself at one point in Revelation. But see Job 38, where it says that when the foundations of the world were laid, "the morning stars sang together, and all the sons of God shouted for joy." I think this is the closest we have in the Bible to a passage equating Lucifer with an angel.
It's important to note that both of these passages are highly poetic in nature, as is the third, the story of the Dragon in Revelation, who is cast out of heaven and makes war with the Church, who is equated to Satan. If the dragon cast out of heaven is the same as Lucifer the Morning Star cast out of heaven, then he is Satan. But it's difficult to say anything for certain, going only on Biblical authority.