I think I missed it but why would they help lucifer to find a vessel?

Bro I think it was cause he is the second most powerful demon king and he had been helping in the study of bringing demon kings to the human realm while giving humans power to fight off the other demons? I think its more complicated than that tho

I not exactly sure but from what I understood, Lucifer is like time bomb,well atleast that’s what sir phillus said. And that if he lost his vessel I guess it’ll mean the destruction of assiha. Well atleast that’s what I got from the conversation.