I gotta say, the whole Lucifer thing in DxD always felt a bit secondary to me. Yeah, Rias and Sirzechs are technically Gremorys who inherited the title, but the narrative weight is almost entirely on the 'Maou' aspect, not the biblical devil archetype. The original Lucifer is basically a backstory device, a reason for the current power structure. Most of the time, it's just a fancy title that makes Rias seem more important in the peerage hierarchy. They talk about the 'original Lucifer' sometimes, but it's like... world-building seasoning, not the main course. The story is way more invested in the current Maou council and their politics, or Rias's personal struggle with her arranged marriage, than digging into what 'Lucifer' truly means in that universe. It's a legacy, not an active role.
Honestly, I think the author knew the 'Lucifer' name carries a lot of baggage and just used it for instant prestige. The real focus is always on the characters wearing the title now—Sirzechs being this overwhelmingly powerful, chill guy who loves his sister, and Rias grappling with the expectations that come with the name. The mythological weight gets traded for shonen power scaling and harem antics, which is fine, but don't go in expecting deep demonic theology.
It works for what the series is, though. It gives the Gremory siblings a built-in reason to be central to the mythos without having to constantly reference some ancient, unseen devil.