Verse 12 introduces a beautiful double entendre into Isaiah’s text that is mostly lost when the word Lucifer enters into the translation. As names have meanings in Hebrew, one must remember that the meaning and the name provide a dual context. In this case, the play is on the meaning of “Lucifer” as the “morning star” (literally shining one). By using the meaning of the name rather than just a personal identifier, Isaiah can speak directly to both Babylon and Satan simultaneously. This is a speech that applies to both.
Both Babylon and Satan are cut down from their former power to oppress nations (v.12).
Both Babylon and Satan had thought themselves so great as to be with the gods, and to be ruler over all.
Both Babylon and Satan thought they were so powerful as to become as God. In the case of Satan, his aspirations are best seen in the account of the book of Moses:
Moses 4:1
1 And I, the Lord God, spake unto Moses, saying: That Satan, whom thou hast commanded in the name of mine Only Begotten, is the same which was from the beginning, and he came before me, saying—Behold, here am I, send me, I will be thy son, and I will redeem all mankind, that one soul shall not be lost, and surely I will do it; wherefore give me thine honor.
In this occasion, Lucifer’s pride wanted the honor of God, certainly a corresponding emotion to Isaiah’s accusation that he wanted to “ascend above the heights of the clouds; [and] be like the Most High.”