Lucifer is an EX-Type Zero that Anne fought during her time with the Northern Order in the seven year interval between Velchees and the start of the Manwha in SE - 430.
It appears to be a ranged attacker, Anne detailing how she was irradiated by the radioactive fallout from Lucifer's particle beams, after her DC Coat was blasted off by it.
It was likely a higher rank Type Zero, quite likely being the last Type Zero, preceding Fear by three years, which was ranked at B-Class or above as mentioned by Dry and Anne:
Anne: "It's probably from when I fought Lucifer a few years ago."
Dry: "It's been three years since a Type Zero of B-Class or higher..."
The large scale battle in which Lucifer and Anne fought in resulted with her as the only survivor from the human forces, but from Leo's commentary, it appears that even then, Lucifer was on the brink of defeat, managing to escaping before Anne could finish him.
After fighting Anne, Lucifer went to absorb the power and armament of EX-Type Zero Satan, ranking up to S Rank in the process.
He reappears later in Knight Fall Ch 2 and gets killed in the battle with Lea Zail and her Knights.