The Great Celestial War is an event which, plot-wise, occurred long before MC arrives in Devildom. It is the name given to the war between God and Lucifer, where Lucifer's rebellion was foiled and all those who took part were banished.
The cause of the war began with Lilith, the youngest sibling and only sister of the seven brothers. Lilith was loved by all her brothers and was especially close to Beelzebub and Belphegor. Whenever Belphegor snuck out of the Celestial Realm, Lilith would follow him, slowly developing a interest in humans just like him.
As time went by, Lilith fell in love with a human, hiding the fact that she was an angel from him. However, the man whom Lilith loved eventually became mortally ill. In an attempt to cure him, she took food from the Celestial Realm and fed it to him; a forbidden act, as angels are not allowed to alter a human’s life. Once their father found out, Lilith was sentenced to be executed. This sparked the rebellion between the Celestial Realm and the seven brothers.
At one point during the war, Beelzebub was forced to choose who to save: his twin brother, Belphegor, or his little sister, Lilith. In the end, Beelzebub rescued his twin brother as a mortally wounded Lilith fell from the sky. Afterwards, Beelzebub blamed himself for Lilith's death, as well as believed that Belphegor blamed him as well for not choosing to save her instead of him.
The brothers' rebellion ended in defeat, and their father banished the brothers from the Celestial Realm. In a fit of rage towards his father, Lucifer tore his own wings from his body, thus resulting in the creation of Satan.
While the six younger brothers believed Lilith died as an angel, instead she had fallen into the Devildom, where Diavolo told Lucifer that he would risk interfering with the Celestial Realm's judgment by saving Lilith, but would save her, only if Lucifer pledged his loyalty to him. Lucifer agreed. Diavolo then had Lilith reincarnated as a human who lived a happy and fulfilling life without any memories of her former life. Lucifer did not tell his brothers that Lilith still lived due to the condition that they were not to contact her, and felt that he alone should carry the burden.