Lucifer Morningstar

Lucifer is the ruler of Hell, the husband of Lilith and the father of Charlie. He can be seen in multiple pictures alongside Lilith and Charlie in the background of the pilot.

Personality
Not much is known about Lucifer at this time due to VivziePop wanting to prevent spoilers for the show's later episodes. However, she has stated that he is 'goofy', and has implied that he has a love for music and instruments.

Charlie
Charlie is Lucifer's daughter. In the pilot, it is implied that Lucifer does not believe in his daughter's plan to rehabilitate sinners. Nonetheless, Charlie did take his words of dealing with unscrupulous folk to heart, such as Alastor.

Lilith
Lilith is Lucifer's wife. It's unknown what their relationship is outside of being married.

Alastor
Lucifer has yet to physically interact with Alastor. According to Vivziepop, Alastor would kind of like him. In Viv's #7 stream, Alastor would like Willy Wonka because he's a jerk, and then she said that Lucifer has a lot in common with Willy (2:13:04).

More than that, Vivziepop and Dave said in Viv's #9 stream(0:48:24) that Alastor in no way would be afraid of Lucifer, though Lucifer may be an intimidating character. They respect each other, and there's mutual respect going on between them.

Trivia

 * The apple tucked in the brim of his hat and on the end of his cane seem to reference the story of Adam and Eve, where a talking snake (often interpreted as being the Devil) persuades the first woman Eve into eating a forbidden fruit, which is often depicted in pop-culture as an apple, resulting in her and Adam being thrown out of paradise.
 * Lucifer's character is based on pop-culture version of the Devil, where he is typically portrayed as being the fallen-archangel Lucifer who attempted to conquer heaven in a great war before being cast down to Hell where he became its ruler and the adversary of God. In some texts, Lucifer is dubbed "Satan."
 * In Hazbin, Lucifer and Satan are separate characters.
 * For full Biblical clarification, Lucifer (Shining One) is only used once throughout the entire Bible in Isaiah 14, where Verse 4 makes it clear that it refers to the King of Babylon, who held similar ambitions to Satan, with Verses 16 to 20 reinforcing that the term refers to a Human King. Thus making Hazbin's depiction of Lucifier & Satan as separate entities Biblically accurate, even if only by accident.
 * In her VIVZIE STREEM- Test Test -#1 live stream, when asked if she can tell fans anything about Lucifer, or at least what his relationship is like with Charlie, Vivziepop said that she can not say very much about Lucifer yet because of it being a little bit too much of a spoiler for the future (especially his relationship with Charlie, which is kind of a big part of the show). The only hint Vivziepop gives regarding Lucifer's personality is that he is goofy and enjoys polka music.
 * When asked if Lucifer is aware of Charlie's idea (indirectly referring to The Happy Hotel), Vivziepop said that she can't say yet because that will be in the show.
 * According to Vivziepop in YouTuber ARTISM PODCAST's Artism Episode 59: VivziePop podcast, Charlie takes very much after her father.
 * Charlie seems to have inherited his rosy cheeks, yellow eyes, fangs, and pale complexion.
 * He is slightly shorter than Charlie.
 * Lucifer can play many types of instruments very well, but according to Vivziepop there is an instrument he has not perfected yet, and is quite bad at it as a result. Additionally, she said that his favorite instrument depends on who the voice actor is.