The author's note at the end said he was, but I'm not sure how it could be, unless they solved the issue of returning back and forth from both worlds. Lucifer first came to this world when he looked 10-ish, but it stated he'd been the demon lord for a while, long enough he and all other demons grew bored and integrated into human society a hundred years ago. Major continuity errors arise with his being Lucifer, but according to the author, he is. ╮(￣▽￣)╭
Or maybe I'm just overthinking a cute story, and it's not that deep. ٩(๑❛ᴗ❛๑)۶
probably just a time skip…
that last couple akechi is definitely lucifer right?? he has the same horns and the same hair!!