One form Lucifer takes in their duel is that of Anti-Life, the End of Everything. Throughout the Silver Age, and into the Modern Age, of DC comics, the Anti-Life equation has been sought by Darkseid, The Great Darkness, as a means to end the chaos of free will, and bring all living things under his dominion.
The names that Morpheous calls Lucifer (Light Bringer, Morning Star) are the names given to the planet Venus in its morning aspect from Roman folklore and the Jewish Bible. It's translated from Hebrew in the King James Bible, meaning "shining one" or "light bearer".
"Nada", the name of Morpheus' ex, translates to "Hope" in some Slavic languages (e.g. Serbo-Croatian).
The much loved Lucifer (2015) Morningstar as played by Tom Ellis and loosely based on the works of Neil Gaiman does not appear in this series with Gaiman stating of Ellis' interpretation "He is so lovable. He is so wonderful. You love him so much that I couldn't sell the world on Tom's Lucifer as being a genuine threat because you'd go, 'Ah, he'd get them all wound up, and then they'd go for a drink" but he continued hoping for a multiverse cross-over where Ellis' and Gwendoline Christie (the Lucifer in this episode) get to meet.
Nada, the name of Morpheus' ex translates to Nothing in Spanish and Portuguese.