As the Devil, Lucifer tires of the millennia he spent being the Lord of Hell, punishing people. Becoming increasingly bored and unhappy with his life in Hell, he abdicates his throne in defiance of his father(God) and abandons his kingdom for Los Angeles, where he runs his own nightclub called Lux and found a job as a police consultant on Chloe Decker's side.
Amenadiel is the eldest child of God and Goddess, born seconds after the Big Bang, he is billions of years old. As an angel child, he played and trained with his siblings. All of his siblings admired, respected, and even feared him.
Mazikeen was one of Hell's most decorated torturers, inheriting a rather sadistic composure and sense of humor. Despite all of this, she is profoundly loyal to Lucifer and whatever decisions that he makes, having left Hell to look after him and always nagging him for his own well-being.
Chloe Decker is a LAPD homicide detective and Lucifer's partner. She is portrayed by Lauren German. She solves crimes with Lucifer after he takes an interest in her because she appears immune to his abilities. She, on her part, finds his "Lucifer-ness" both intriguing and hard to deal with.
Daniel "Dan" Espinoza was a central character on Lucifer and served as a homicide detective in Los Angeles, working as a member of the L.A.P.D. Dan disliked Lucifer quite a bit, due to Lucifer calling him "Detective Douche" and his connection to Dan's ex-wife, Chloe Decker, and daughter, Trixie.
Linda Martin is a therapist living in Los Angeles and serves as a central character in Lucifer. Throughout the series, Lucifer Morningstar, the ruler of Hell, seeks her counsel on a consistent basis, usually involving personal issues with Chloe Decker or his family.