Lucifer fell from heaven because of his pride (Jerome). The enemy is a fallen being of light. The one fallen from heaven cannot be Nebuchadnezzar or any other human being (Origen). Lucifer descended from better to worse in his fall from heaven (Eusebius). Lucifer fell from heaven because he wanted to be like God (Jerome). Pride was the reason for Lucifer’s fall (Augustine). Nebuchadnezzar was destroyed because of his pride (Aphrahat). Lucifer fell not because of any sinful actions but because of his prideful tongue (Jerome, Ambrose, John Cassian). Death comes to all, showing the limitation of human pride (Chrysostom). The devil, a robber and accuser, can find no fault in Christ (Augustine), nor can he take the exalted place of God (Cassiodorus). God’s wrath on obstinate sinners is unbearable (Verecundus). God uses even bad circumstances for good, and his will prevails (Chrysostom). The flying serpent, or basilisk, can destroy even from a distance (Gregory the Great). Christians must guard against the sin of pride (Ambrose).
Origen:
It is most clearly proved by these words that he who formerly was Lucifer and who “arose in the morning” has fallen from heaven. For if, as some suppose, he was a being of darkness, why is he said to have formerly been Lucifer or lightbearer? Or how could he “rise in the morning” who had in him no light at all?… So he was light once … when “his glory was turned into dust.” On First Principles 1.5.
How can we possibly suppose that what is said in many places by Scripture, especially in Isaiah, about Nebuchadnezzar is said about a human being? For no human being is said to have “fallen from heaven” or to have been “Lucifer” or the one who “arose every morning.” On First Principles 4.3.9.
The term Lucifer is taken in early translations (mostly from Vulgate I guess, as mentioned by Jerome) instead of a more literal and direct "morning star" in Hebrew because church fathers doubt that "morning star" is a correct understanding, especially as expressed by Origen.
Jerome:
For greater ease of understanding we translated this phrase as follows: “How you have fallen from heaven, Lucifer, who arose in the morning.” (instead of "morning star")
Till Augustine, it seems that a firm consensus is reached that Lucifer is the devil.
Augustine:
For example, what is said in Isaiah, “How he is fallen from heaven, Lucifer, son of the morning!” and the other statements in that context that speak of the king of Babylon are of course to be understood of the devil.