first off, theres absolutely no certainty tha Lucifer showed you a different aspect of himself as Melek, I personally dont know if they are the same, but reading on Melek, his description is similar to Archangel lore, now…in my experience and opinion, Lucifer is an ex Archangel, a Dark Seraphim, so i could see the connection
however, i just read this:
The Yazidi consider Tawûsê Melek an emanation of God and a good, benevolent angel and leader of the archangels, who was entrusted to take care of the world after he passed a test and created the cosmos from the Cosmic egg. Yazidis believe Tawûsê Melek is not a source of evil or wickedness. They consider him to be the leader of the archangels, not a fallen nor a disgraced angel, but an emanation of God himself.
which in my experience and opinion is not correct, as Lucifer WAS an Archangel, but hes not anymore ime and imo.
theres also this:
Since the late 16th century, some Muslims have accused Yazidis of devil worship due to the similarity between the Quranic story of Iblis and the account of Tawûsê Melek’s refusal to bow to Adam. Whereas Muslims revile Iblis for refusing to submit to God and bow to Adam, believing that his defiance caused him to fall from God’s grace, Yazidis revere Tawûsê Melek for loyalty towards God and believe that God’s command to Tawûsê Melek was a test to see who is truly devoted to God alone. This narrative led to many misinterpretations, also made by Western scholars, who interpreted the Yazidi faith through their own cultural influences. Further accusations derived from narratives attributed to Melek Taus, which are actually foreign to Yazidism, probably introduced by either Muslims in the 9th century or Christian missionaries in the 20th century. Accusations of devil worship fueled centuries of violent persecution, which have led Yazidi communities to concentrate in remote mountainous regions of northwestern Iraq. The Yazidi taboo against the Arabic word Shaitan (الشیطان) and on words containing the consonants š (sh) and t/ṭ have been used to suggest a connection between this Tawûsê Melek and Iblis, although no evidence exists to suggest Yazidis worship Tawûsê Melek as the same figure. The “Yazidi Black Book”, written by Western Orientalists, directly identifies Melek Taus with Azazil or Azrail. However Yazidis identify Melek Taus with Jibrail (Gabriel). In one Arabic manuscript, the name “Jabrail” is used in secondary reading, instead of “Melek Taus”. The title “peacock of paradise” was also applied to Gabriel among Islamic traditions.
now, that is a muslim point of view that i personally am not sure how correct it is
to me, Lucifer is the Lord of Hell, the Ex Archangel, the Dark Seraphim, there are weaker and stronger beings than him
this thing with lumping him the same as shiva and loki and etc, to me is sometimes ridiculous, but i can see the supposed connections with Melek, however, i believe they are different, as Lucifer is the Lord of Hell, ex Archangel, while Melek is an Archangel still.
My advice to you is keep working with Lucifer using his famous sigil (the famous one) and enn, and dont conflate Melek with Luce, that would just be confusing imo.