What is the role of Lucifer in the Heavenly realm?
ANSWER
Lucifer is the "anointed cherub", the word Lucifer is not a literal name taken from the Latin Vulgate translation of the word "morning star", it is a "title or a role" given by God to a chosen angel to fulfill His Will.
The role given by God to the "anointed cherub" is to guard the Holy Mountain by expanding his wings that can cover whatever is there in the Holy Mountain.
Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire. (Ezekile28:14)

Looking at the picture can we infer what will be the problem, if only one "anointed cherub" will guard it? Lucifer will expand his wings to cover the "Ark of the Covenant"? Lucifer will position himself at the center of the ark and then will spread his wings like eagle to cover the "Ark of the Covenant". What is the problem with that position? Angels instead of worshipping the "Ark of the Covenant" they see first Lucifer and the angels are bowing not to Lucifer but to the Holy One in the Holy Mountain. After the Fall of Lucifer, the Ark of the Covenant is now visible because the two anointed cherubs that guard it now position themselves at two sides.
But, why God would Will that the "Ark of the Covenant" be covered or hidden from the angels in the Holy Mountain of God?
St.Paul words reveals that God conceal from the angels the "hidden Wisdom of God". And that "Jesus became the Wisdom of God".
"It is because of him that you are in Christ Jesus, who has become for us wisdom from God—that is, our righteousness, holiness and redemption." (1Corinthian1:30)
God concealed "His Wisdom on Man's Salvation" that's why when Lucifer was cast out and take a new role of Satan an opposer of the Will of God, Satan did not know that the "hidden Wisdom of God" is the Jesus Christ suffering and dying At the Foot of the Cross.
"Wisdom is the Cross and the Cross is Wisdom" (St.Montfort)
In closing, the "anointed cherub" did not fulfill the "Will of God" as "light bringer or Lucifer" in the Holy Mountain, but instead had shown "Pride & Disobedience". That's why St.Jerome depiction of Isaiah14:12-ff attributing the translation of Hebrew word "morning star" to "Lucifer" in Latin carries the key word "Will of God" vs. the "I Will" of Lucifer.
Lucifer the chosen angel cherub is the "light-bringer" he was "anointed to fulfill the Will of God to bring the Light of God to all the angels. Lucifer bear the Light of God externally only and failed in his role that lead to his downfall.
While in contrast, the chosen Woman, that would "bear the Logos" in Her pure womb had embraced the "Will of God" and successfully bring Jesus Christ as the Light of God in the whole world, saying the famous 'Fiat;
" And Mary said: Behold the handmaid of the Lord; be it done to me according to thy word. And the angel departed from her. (Luke1:38)
FURTHER EXPLANATION
First of all, we need to answer where does the name of Lucifer came from?
Lucifer (UK: /ˈluːsɪfər/ LOO-si-fər; US: /-sə-/; 'light-bringer') is a Latin name for the planet Venus in its morning appearances, and is often used for mythological and religious figures associated with the planet. Due to the unique movements and discontinuous appearances of Venus in the sky, mythology surrounding these figures often involved a fall from the heavens to earth or the underworld. Interpretations of a similar term in the Hebrew Bible, translated in the King James Version as "Lucifer", led to a Christian tradition of applying the name Lucifer, and its associated stories of a fall from heaven, to Satan. Most modern scholarship regards these interpretations as questionable, and translates the term in the relevant Bible passage (Isaiah 14:12) as "morning star" or "shining one" rather than as a proper name, "Lucifer".1
As a name for the Devil, the more common meaning in English, "Lucifer" is the rendering of the Hebrew word הֵילֵל (transliteration: hêylêl; pronunciation: hay-lale)[2] in Isaiah (Isaiah 14:12) given in the King James Version of the Bible. The translators of this version took the word from the Latin Vulgate,[3] which translated הֵילֵל by the Latin word lucifer (uncapitalized),[4][5] meaning "the morning star, the planet Venus", or, as an adjective, "light-bringing".[6]
As a name for the planet in its morning aspect, "Lucifer" is a proper name and is capitalized in English. In Greco-Roman civilization, it was often personified and considered a god[7] and in some versions considered a son of Aurora (the Dawn).[8]
In classical mythology
Lucifer (the morning star) represented as a winged child pouring light from a jar. Engraving by G.H. Frezza, 1704
In classical mythology, Lucifer ("light-bringer" in Latin) was the name of the planet Venus, though it was often personified as a male figure bearing a torch. The Greek name for this planet was variously Phosphoros (also meaning "light-bringer") or Heosphoros (meaning "dawn-bringer").[23] Lucifer was said to be "the fabled son of Aurora[24] and Cephalus, and father of Ceyx". He was often presented in poetry as heralding the dawn.[23]
The Latin word corresponding to Greek "Phosphoros" is "Lucifer". It is used in its astronomical sense both in prose[25] and poetry.[26] Poets sometimes personify the star, placing it in a mythological context.[27]
In Christianity(Background)
In the Book of Isaiah, chapter 14, the king of Babylon is condemned in a prophetic vision by the prophet Isaiah and is called הֵילֵל בֶּן-שָׁחַר (Helel ben Shachar, Hebrew for "shining one, son of the morning").[19] who is addressed as הילל בן שחר (Hêlêl ben Šāḥar),[37][38][39][40][41] The title "Helel ben Shahar" refers to the planet Venus as the morning star, and that is how the Hebrew word is usually interpreted.1[42] The Hebrew word transliterated as Hêlêl[43] or Heylel (pron. as Hay-LALE),[44] occurs only once in the Hebrew Bible.[43] The Septuagint renders הֵילֵל in Greek as Ἑωσφόρος [45][46][47][48][49] (heōsphoros),[50][51][52] "bringer of dawn", the Ancient Greek name for the morning star.[53] Similarly the Vulgate renders הֵילֵל in Latin as Lucifer, the name in that language for the morning star. According to the King James Bible-based Strong's Concordance, the original Hebrew word means "shining one, light-bearer", and the English translation given in the King James text is the Latin name for the planet Venus, "Lucifer",[44] as it was already in the Wycliffe Bible.
https://en.wikipedia.org/wiki/Lucifer
So, from wikipedia we can summarize that the name "Lucifer" is a translation of the word "morning star" into Latin, and it also means in Hebrew as the "shining one, light-bearer".
We can see that from the description, the Latin word "Lucifer" is not a "name" literally but a "description or a title".
Now, if Lucifer is a name that denotes a role, title or a description, who gave him that title? Definitely God in the Heavenly Realm is the only one who have the right to gave each angel their name because He is the Creator, just like when Adam named all the creatures because God gave him the authority to name them. God is the Supreme, Eternal Authority as Creator of Heaven & Earth.
The question now is, when was God gave the title or role to the beautiful angel who was described in Ezekiel28:12 as perfect in beauty and full of wisdom?
Like the Holy Name of Jesus and Mary it was God who named them in eternity, and their names implied a "role or anointing" for them to fulfill the "Will of God". The other names in the realms of angels that scriptures identified in Hebrew word are Michael. Gabriel and Raphael and these three angelic names connotes each a description of their "power and role" to fulfill the "Will of God".
Now, in Ezekiel28:14 God has "anointed" a "cherub". We know that when God "anointed" a creature the purpose is for that creature to fulfill His Will.
What is the role or the "anointing" given by God to the "cherub" who already was bestowed upon a gifts of perfect beauty and full of wisdom? Let's look at Ezekiel words;
Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire. (Ezekile28:14)