Azazil is considered to be another name for Melek Taus according to the Yazidi Black Book (which is considered to be one of the two holy books within that culture/religion).
If you read the stories of both the figures in question there are strong parallels between the two. According to some denominations, Azazil is destined to be redeemed by God just as Melek Taus was within his own story.
There is the argument that it was meant to be translated to Azrael but I believe that this is mostly a front and doesn’t really add up due to there already being an angel of death separate from Melek Taus as well as the stories between the two figures not correlating at all.
Lucifer could only be equated to Melek Taus through Azazil’s association honestly (I personally don’t think Lucifer is Azazil but if someone does this is how people can come to a reasonable conclusion).