While Lucien continues to fight the Leviathan, pushing his body and soul to the limit to try to understand more about the power Aylin found within the golden naginata, he doesn't notice the time passing.
Although progress towards the next golden gate within the naginata is being slow, his progress with Oya and Helena is rapidly evolving within the purple world.
As he only has them to recharge his energy, Helena and Oya are always full of his demonic energy, and that's why they're always sleeping while he's fighting the Leviathan.
Also, the creature's brutal blows always knock Lucien tens and even hundreds of meters away, and he doesn't even notice that with each fight, they move farther and farther north.
Meanwhile, thousands of miles away, the Sea Devil continues sailing at high speed. Madelyn, already exhausted, is still creating powerful wind waves along with the ship's magic sails.