There is truth that there are two "fallen angel" events. The first being pre-Flood in Genesis 6 which had to have happened after the Garden of Eden due to the fact it is written this happened when daughters were born unto men. The second being the prophesied event in Revelation which this topic is about.
As for Satan falling the first time, this is not in the Bible. Genesis 3 is the first time that Satan is mentioned, and very bluntly is stated he is a subtil beast of the field which the Lord God created, which means he is an animal.
As for the reference to King of Tyre, this is not a reference to Satan. The prophecy is very clear that it is about an ancient king of Tyre whom was at one time a good man until iniquity was found in him. Therefore the Lord destroyed him and his famous ancient city. Behold, this prophecy all ready came to pass and the city of Tyre is a ruin and waste unto this day. One will also note Ezekiel does not use the term lucifer in this prophecy.
Additional support for the fact the dragon is not the same as any of the people referred to as lucifer is found in Revelation 12. When describing the War in Heaven the dragon's titles are all on full display and those titles are Satan, Devil, and deceiver of the whole world. Clearly the Bible never uses the title Lucifer to refer to the dragon. Lucifer mean light-bringer, dawn-bringer, morning star, etc. and we know there is no light in the dragon that is called the Enemy and the Liar.