Lucifer Morningstar/Relationships

Charlie Morningstar
Charlie is Lucifer's daughter. In the pilot, it is implied that Lucifer does not believe in his daughter's plan to rehabilitate sinners, with Charlie saying, "I think Dad was right about me," when calling Lilith about her failed interview. According to Faustisse, despite having immense love for his family, Lucifer is not a good father, but he loves his daughter deeply. Nonetheless, Charlie did take his words of dealing with unscrupulous folk to heart, such as Alastor.

As shown in "Dad Beat Dad", Lucifer cares for Charlie deeply and loves her very much. Albeit, he has difficulty showing it and properly expressing his affection for her due to his other issues. Lucifer himself wishes to spend more time with Charlie and desires to feel close to his daughter as they once were when she was child, as seen where he was delighted when Charlie invited him over to her Hotel, taking it as Charlie wanting to spend more time together.

Later, Lucifer himself would show jealousy towards Alastor when the latter began showing his "deep" bond with Charlie for his support of her dreams and goals of the Hazbin Hotel. As shown, Lucifer was obviously threatened by Alastor taking Charlie away from him and was incensed when Alastor pointed how little support Lucifer had given Charlie in her dreams, with Lucifer becoming increasingly insecure of his father-daughter bond with her and began to fight with Alastor to get Charlie's attention.

Lilith
Though little is known about their actual relationship outside of being married, they are revealed in "Dad Beat Dad" to have separated.

Razzle and Dazzle
Razzle and Dazzle were gifted to Charlie by Lucifer during her childhood to act as her personal bodyguards. Razzle and Dazzle are protective of Charlie and the rest of her family.

Hell
Lucifer is the King and creator of Hell and thus rules over all the Demons that reside there. However, despite his role as its king, Lucifer himself hardly ever “rules” over his subjects and instead leaves them primarily to their own devices, leading to many other demons, such as the Overlords, Seven Deadly Sins and Ars Goetia Demons to do the actual ruling of Hell in his place.

Sinners
As revealed in “Dad Beat Dad“, Lucifer in truth, despises the Sinner Demons who reside in the Pride Ring of hell and he cares little for what happens to them.As shown where it has been heavily implied in the series that he does not truly rule over Pentagram City and instead leaves them to their own devices, leading to the rise of many Overlords who run the city in his place. Due to his absent presence, many of the Sinner Demons don’t respect his or his family’s authority despite being the royal family of hell, albeit, they are at least aware of Lucifer’s immense power, leading them to leave his daughter alone despite how much she annoys them.

As shown from his conversation with Charlie, Lucifer considers all the Sinner Demons of hell to be "violent, destructive psychopaths, hellbent on causing as much pain and destruction as possible" and believes it is impossible for them to be redeemed. With Lucifer himself even hinting that he regrets his role in ever giving them freewill due to what they had done with it and how terrible they made everything become. This cynicism and apathy to the Sinner Demons has even implied to have lead to Lucifer actively cooperating with the Exorcists in the Extermination in order to handle hell’s overpopulation.

Hellborn Demons
On the other hand, Lucifer had been implied to have a completely different attitude towards the Hellborn races of hell. As stated by Lute, Lucifer had arranged for a pardon for them with Heaven, insuring that the Hellborn races and thus the other Six Rings of Hell, are untouched by the Exorcists during the yearly Exterminations. Hinting that Lucifer cares for them more in comparison to the Sinner Demons of the Pentagram City.

Alastor
In "Dad Beat Dad", Lucifer showed jealousy towards Alastor when the he began showing his "deep" bond with Charlie for his support of her dreams and goals of the Hazbin Hotel. Lucifer was obviously threatened by Alastor taking Charlie away from him and was incensed when Alastor pointed how little support Lucifer had given Charlie in her dreams, with Lucifer becoming increasingly insecure of his father-daughter bond with her and began to fight with Alastor to get Charlie's attention.

Vivziepop and Dave Capdevielle said that Alastor in no way would be afraid of Lucifer, though Lucifer may be an intimidating character, there's mutual respect going on between them.

Mammon
Mammon considers Lucifier as his "friend". Though little is known whether or not Lucifer affirms this friendship with Mammon.