Chapter 13 describes both the literal and spiritual fall of Babylon. As is the usual modus operandi with Isaiah, he uses dualism to prophesy of events. In this case, Babylon is a real nation that is wicked and is utterly destroyed. Spiritually speaking, Babylon represents the world and its desires. In the Last Days, the wicked will be completely destroyed as was Babylon the nation.
A Banner, an Ensign
In Isaiah 13:2-5, the God issues a call to His people to gather to fight Babylon. The "sanctified ones" gather and their gathering is like a "noise of a multitude in the mountains, like as of a great people; a tumultuous noise of the kingdoms of nations gathered together." And then the bombastic statement: "the Lord of hosts mustereth the host of battle."
In a spiritual sense, we must do our part to heed the call to the great rally. We can begin by conquering the enemy within or the natural man. In the October 2000 General Conference, James E. Faust said the following, " President Joseph F. Smith taught us: “Our first enemy we will find within ourselves. It is a good thing to overcome that enemy first and bring ourselves into subjection to the will of the Father, and into strict obedience to the principles of life and salvation which he has given to the world for the salvation of men.” In simple terms, this means that we need to strengthen the good within us and to overcome the temptations of Satan. The direction finder is sure. Alma tells us, “Whatsoever is good cometh from God, and whatsoever is evil cometh from the devil.” (James E. Faust, “The Enemy Within,” Ensign, Nov 2000, 44–46)
As we overcome Satan's fiery darts (see Eph 6:16; 1 Ne. 15:24; D&C 3:8; 27:17) we will lead a life of righteousness by example and we will have "confidence" (D&C 121:45) and can fight the adversary and his devious teachings.
The Destruction of Babylon
The fall of Babylon (physically and spiritually) will be so complete, that it will never be rebuilt or inhabited (Isaiah 13:19-20). So many inhabitants (and spiritually wicked people) will be destroyed that man will be rarer than gold. Those that are left will be the foundation for a new millennial reign (Isaiah 13:12).
Again, Isaiah uses dualism to describe the downfall of Babylon's king who is synonymous to Satan - both would fall and eventually be forgotten.
Lucifer was a "son of the morning" and probably held a high rank in the counsels of heaven. But he rebelled against God and sought to take God's power to himself. "I will sit also upon the mount of the congregation, in the sides of the north." The CES Institute manual notes that Bible commentators Keil and Delitzsch translated the word "congregation" as "assembly of gods."
Satan was cast to earth where he continued to wage war on the children of men. Eventually he will be thrust to Hell "to the sides of the pit" and all will look on him and wonder "is this the man that made the earth to treble, that did shake kingdoms?" (Isaiah 14:16). Kings will have memorials and tombs and will be resurrected, but Satan will have no memorial and no body. He will be cast in to outer darkness forever and will lose all power (D&C 133:73).