Lucifer was Satan's name - given to him by God - before he became the devil.
This is an example of how folklore and myth can shape people's way they approach things. Here in this modern age with printed scripture for over 400 years and with the internet at our disposal people still cling to myth over knowledge that Satan's proper name is Lucifer.
Lucifer is a Latin word and in the Latin text it is used for both Satan and Jesus. It is just a regular word and it means light bearer but we would rather believe the myth and legend that it's Satan's proper name given to him before his fall. I would rather call Jesus Lucifer .
While it is true there is a tiny "hint" of truth in your statement - it concludes with gross error none-the-less.
As if you had never read Isaiah 14 in your life.
I prefer the actual Bible.
==================== Lucifer -- Satan-- the Devil
Isaiah 14
The Fall of Lucifer
12 “
How you are fallen from heaven,
O Lucifer, son of the morning!
How you are cut down to the ground,
You who weakened the nations!
13 For you have said in your heart:
‘
I will ascend into heaven,
I will exalt my throne above the stars of God;
I will also sit on the mount of the congregation
On the farthest sides of the north;
14 I will ascend above the heights of the clouds,
I will be like the Most High.’
15 Yet
you shall be brought down to Sheol,
To the lowest depths of the Pit.
16 “Those who see you will gaze at you,
And consider you,
saying:
‘
Is this the man who made the earth tremble,
Who shook kingdoms,
17 Who made the world as a wilderness
And destroyed its cities,
Who did not open the house of his prisoners?’
18 “All the kings of the nations,
All of them, sleep in glory,
Everyone in his own house;
19
But you are cast out of your grave
Like an abominable branch,
Like the garment of those who are slain,
Thrust through with a sword,
Who go down to the stones of the pit,
Like a corpse trodden underfoot.
20 You will not be joined with them in burial,
Because you have destroyed your land
And slain your people.
The
brood of evildoers shall never be named.
No doubt the Isaiah 14 text is figuratively referring to Satan and that is something I have never denied. Literally the text is talking about the King of Babylon
Well literally the King of Babylon was not named Lucifer. Whereas Lucifer's name really was Lucifer.
Literally the king of Babylon did not fall from heaven - whereas Lucifer did and was cast down to earth after literally losing the war in heaven.
But as you say "the local" application is the King of Babylon - whereas the literal application is to Lucifer without superlative or exaggeration.