In the second Book of Enoch, Satanael, also known as Sataniel or Satanail, is mentioned as an archangel that lead the fallen angels that rebelled against God, by refusing to bow to the human Enoch, leading to his imprisonment. Due to his name and role, he is considered an interpretation of Lucifer.
In some Gnostic traditions, Satanael is said to be an angel that once served Yaldabaoth. He rebelled when he realized that Yaldabaoth was not the true God and granted humanity the knowledge to liberate themselves from Yaldabaoth. In other traditions, he is said to have created the material universe as a second heaven to rule over and became the God of the Old Testament, making him an interpretation of the Yaldabaoth.
According to the beliefs of the Cathars, a notorious medieval heretical creed, Satanael (or Satanel) was the angelic name of Satan before Michael the archangel removed the -el suffix (signifying the loss of his angelic nature) and sealed him in Hell. In this interpretation, Satanael is the radical opposite of God and the ruler of the material world.
During the final events of the Monolith, Spooky will appear at the ruined transmission tower, possessed by Satanael, who plans to take over now that Azazel and Shemyaza are gone. Taunting the party, he suggests they "thank him for letting them die by their friend's hand," which he uses as a puppet and human shield in the boss fight.
Satanael can be fused in New Game Plus. The protagonist must be level 95 and perform an advanced fusion using Arsène, Anzu, Ishtar, Satan, Lucifer and Michael. The protagonist can bypass the level requirement if the Confidant with Caroline and Justine has been maxed. Due to the ingredient requirements, the protagonist must have completed the Confidants with Ann Takamaki, Hifumi Togo and Yuuki Mishima at some point, and have been down the true ending route, as to fuse Metatron, one of the Personas needed to summon Lucifer, the Confidant with Goro Akechi needs to be maxed out (this is done when he is fought in Shido's Palace from November 25th at the earliest to December 16th at the latest). Satanael is the only Persona to learn the Victory Cry skill, as well as one of three to learn Riot Gun, Cosmic Flare, Heat Riser and Unshaken Will. Itemizing Satanael through Electric Chair execution yields the Paradise Lost knife, the ultimate melee weapon for the protagonist. A hidden achievement will be unlocked once Satanael is fused in the original. In Royal, during a Fusion alarm, a stronger version of the Paradise Lost knife can be obtained.
Satanael's role and summoning in Persona 5 is based on the series' interpretation of Lucifer, where he is summoned to champion freedom and chaos against the tyranny of Yaldabaoth's order. His summoning for the final battle even has him do the pose of Kazuma Kaneko's demon Lucifer artwork from Shin Megami Tensei II.
Satanael's fusion requirements in Persona 5 are not as long a list as the requirements for Izanagi-no-Okami, but make up for it in sheer expense; requiring anywhere from 800k to over 1 million yen to re-summon the component parts alone and not counting the extra money needed if the fusion is done under its base level of 95.
Satanael's Tyrant's Mind is the only "Amp" skill that can overcome the 2.0x damage limitation in the game, although there are traits that overcome it too.
Satanael's Trait, Pagan Allure, has a 50% amp on all magical abilities, although this trait doesn't overcome the 2.0 limit, it can be used to overcome it using Tyrant's Mind and Magic Ability, reaching a 2.34x damage in up to 6 different magical skills.