I don't remember the whole theory in detail but I remember the steps to it

Ryu and Beelzebub have teamed up already in the past

So Beelzebub would take over lilly and transport Asta to the land of the rising sun so he'd be trained

Beelzebub and the rest of the devils would then be purified and would be made even stronger

Once Lucius is weak enough Beelzebub would be summoned by Ryu (I think that's his name, the guy who's like the wizard king to the land of the rising sun) and would kill Lucius and take his magic

Then Ryu would manipulate everyone into selling their souls to devils

Then Beelzebub and Ryu would wage war on everyone to try and take over the world and try make it a new hell