Lucifer (also known as 'Satan') is the 1i (or No.1) demon of the Reverse Kabbalah. He was sealed within Jio Freed (aka the FREEDOM). He was one of the twenty scientists who were working on the Solomon, but he tried to take control of the program for his own uses, and was ultimately defeated by Adam and Eve.
Lucifer was one of 72 scientists in an organization known as Solomon which sought to understand the greater secrets of the universe by following the breakdown of all the energy of existence. So they created the Kabbalah in order to control the energy but when Lucifer tried to take the power of the 1i Kabbalah his body was destroyed and his consciousness was sealed within the Kabbalah's "Freedom" program which took the form of a young human named Jio Freed.
For most of Jio's life he was unnaware that he was the host to the No.1 demon, however on occasion Lucifer would take control and kill the inhabitants of Jio's village to turn them against him and plunge him into the darkness so that he could one day break free. When Jin made friends with Jio and even promised to be friends with him, Lucifer in turn killed Jin's parents in order to stop this friendship and turn Jin and Jio against each other. A few years later, after Jio had left the village, Jio came into contact with Cross Blancia, sensing that Cross was the No.1 angel and his greatest threat he moved to kill him and Corss's sister Lily (a copy of Solomon's Key) however Cross survived the explosion and vow to one day kill Jio.
During Jio's battle with the fake Satan, Lucifer briefly took control to save Jio's life. This was witnessed by Ruby who became Jio's friend in order to help him deal with Satan inside of him.
Entotsu City Arc
Early on in the series he gave Jio some of his power in the form of Number of the Beast which is found on his left hand. The only problem with this is that every time Jio used this O-Part, the energy that he absorbed helps fuel Satan's presence in the physical world thus allowing him to eventually take over Jio's body
Dust Ruins Arc
While not actually appearing in person persay. There are hints on his pressense, such as when Mr. Wick reveals the meaning behind the ruins of the Kabbalah, and later when he notes the tattoo on Jio's hand. Later on just before Kujaku was about to kill Jio, Lucifer tried to emerge to save him (as he would also die if Jio were to die) this is evidence by Jio's black-half of his hair turning white and if it had not been for the timely arrival of Kirin forcing Kujaku to flee and in turn Lucifer retreated into Jio's subconscious for unknown reasons.
There are heavy hints that Lucifer may be the most powerful being in the entire 666 Satan world, or even universe. The fact that he was powerful enough to frighten or shock characters such as Kujaku and Wise is just a hint of his absolute powers. Unlike the other angels and demons revealed so far Satan is the only one to possess multiple forms; and his various forms include demonic and angelic features similar to the other demons and angels; as sometimes he appears with angelic and demon wings. Satan has shown use of various undefined powers throughout the series. He once used some form of telepathy to invade Ikaros' mind and frighten him via presenting an image of one of his demonic forms enveloping him. He has occasionally used telekinesis and once used it to break Cross's wrist to prevent him from using his rings. by roaring (rather loudly) he is able to produce a large shock wave. He once used a powerful beam attack from his mouth to damage Mekisis. He is able to elongate his arms and tentacles on his back to seemingly limitless lengths. And finally he is able to regenerate otherwise fatal wounds; though his regenerative abilities seem to be limited to how much energy he has absorbed from his left hand.