Past

Lucifer and Lilith are banished to Hell
Prior to the creation of the Earth, Lucifer was an angel, said to be a dreamer with fantastical ideas for all creation. However, the elders of Heaven saw him as a troublemaker who posed a threat to the order of their world. He watched as the angels began to expand the universe without him and that includes the creation of Adam and Lilith. After Lilith left Adam, Lucifer met her in the Garden of Eden and the two dreamers fell in love with each other. Lucifer, with Lilith, wanting to share the power of free will, offered Adam's second wife, Eve, the Fruit of Knowledge. It was with this act evil made its way into the Earth which subsequently created Hell. As punishment, both Lucifer and Lilith were sent to Hell, where Lucifer could only see the worst of humanity and the horrific results of his actions. Ashamed, Lucifer lost his will to dream.[1]
In Hell, now a fallen angel, Lucifer became the ruler of all Hell on the basis of his angelic power,[2] ruling over all the Demons that reside there. At an unknown point, Lucifer became part of an order of powerful demons called the Seven Deadly Sins, each member embodying a sin, with his being Pride.
At some point, he started a successful theme park called Lu Lu World that proved to be quite popular with the denizens of Hell. Another of the Sins, Mammon, created a rip-off of his theme park called Loo Loo Land, claiming to be a friend of Lucifer.[3]

Lucifer playing with Charlie
At some point, he married Lilith, and later fathered a daughter named Charlie Morningstar with his wife.
When negotiating the terms for the Extermination, Lucifer successfully obtained a pardon for every Hellborn demon in Hell, including Charlie, while making it clear only Sinners would die at the hands of the Exorcists.[1]
At another point, Lilith left Lucifer for unknown reasons, which sent Lucifer into a deep depression and isolated himself from his kingdom and daughter as a means to cope. The reclusive Lucifer now spent his time in his home coping by crafting rubber ducks, mostly inactive ruling over Hell.[4]

Lucifer's old throne
After abandoning his duties as king of Hell, Satan took his place as ruler of the Sins and spread the lie that he ruled the endless darkness before the fall of Lucifer. Before leaving, Lucifer left a crying rubber duck on his throne with a note saying thaht he would be back some day.[5]
Hazbin Hotel pilot
In the pilot's opening song, shadowy figures resembling him appear.

Lucifer sitting with the Overlords after the Extermination
During Charlie's fireworks display after the Extermination, Carmilla Carmine, Zestial, and Zeezi are seen watching from a window along with a red-eyed silhouetted figure that strongly resembles Lucifer.
He is later mentioned in Charlie's voicemail to Lilith.
Several photos of him can be seen throughout the Happy Hotel, most notably a family portrait that catches Alastor's attention.
Hazbin Hotel Season 1
"Overture"
Charlie receives a phone call from her father informing her that the leader of the Angel Army wants to meet and asked if she could go to the meeting in his stead.
"Dad Beat Dad"
After making a rubber duck with the ability to breath fire he receives a call from Charlie, making him both nervous and overjoyed. She asked him if he could arrange her to meet heaven's higher-ups but he promptly refuses, then is invited to the Hotel. Upon arriving at the hotel, Lucifer quickly greeted Charlie and hugged her, then was introduced to the staff and residents in the hotel, including Alastor, with whom he developed an instant rivalry through insults.

Lucifer competing against Alastor
He gets in an argument with Alastor over Charlie until being interrupted by Mimzy. Afterwards, Lucifer was guided through the hotel by Charlie, Alastor, and Vaggie. On the balcony, Lucifer was honest with his daughter, telling her that the sinners were horrible, emphasizing the fact that he gave them free will and committed wrongs with it. When the loan sharks pursuing Mimzy attack the Hotel, Lucifer pointed out the chaotic nature of sinners to his daughter.

Lucifer and Charlie reconcile
Charlie lamented that Lucifer doesn't believe in her prompting Lucifer to explain his troubles with heaven, and both remember how they had a good time until Lilith separated Charlie from him. Wanting to get to know each other better and start fresh, Lucifer and Charlie reconcile and reconnect their relationship, and Lucifer agrees to arrange a meeting with Heaven's higher-ups.
"The Show Must Go On"

Lucifer and Charlie vs. Adam
He attacked Adam before the latter could seriously injure or kill Charlie. He apologized to his daughter for being late and comically threatened Adam by saying that he was going to "fuck you" instead of "fuck you up", much to everyone's dismay (except Angel Dust and Valentino's). He proceeded to toy with and berate the angel. Angered that Adam destroyed the Hotel and that he tried to attack him and Charlie from behind, Lucifer unleashed his full demonic form and mercilessly beat up the angel until Charlie stopped him, saying that Adam had enough.

Lucifer shares a hug with Charlie and her friends
After Adam's death, he ordered Lute to take the exorcists and go back to Heaven, and then asked the hotel gang if they wanted pancakes, with Niffty being the only one who raised her hand. Impressed by Charlie's achievements, he promised to help her in her future endeavors, starting by helping rebuild the Hotel and by moving in.[6]
References
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