These verses have dual meanings. Latter-day Saint readers are much more familiar with the description of Lucifer as a pre-moral being who fell because of his pride. It certainly has that meaning.
In the context of Isaiah’s prophecy, however, the meaning that was most obvious to the early readers was that the powerful kings were brought down low. The previous verses spoke of the kings of earth in hell. This address is for a specific king, either of Babylon or Assyria, depending upon how the prophecy is read.
It is that king who thought himself so great as to be almost a god. It was not uncommon in the ancient world for a ruler to be thought divine. That most powerful of earthly kings would be brought down in the ultimate reversal. He will become as the other kings of the earth, who spoke so weakly in the previous verses.
The reversal is that the king who once made the earth to tremble and shook kingdoms will be brought down to the weakness of death.