Depending on who you ask, you will get a different answer on who Lucifer is. Christian's will tell you that Lucifer was an angel that fell from grace (due to Pride) and became Satan and/or the Devil. Satanists and Luciferians will tell you a similar story, and some will view him as one of the Prince's of Hell and an embodiment of enlightenment, freedom and knowledge.
You may also hear others say that Lucifer is Attar in Sumerian mythology or that you can find him in Roman mythology as Lucifer, the son of Aurora and the personfication of the morning star. Likewise, you would see him in Greek mythology as Phosphorus, son of Eos and personfication of the morning star.
Some Neo-Pagans, typically those influenced by Aradia, the Gospel of the Witches, may understand Lucifer as the father of Aradia and brother/lover of Diana. Additonally, some traditional witches may view Lucifer as a guise of the Witch Father.
Some Satanists, Luciferians or Pagans might associate Lucifer with deities such as Enki (Sumerian god of wisdom/knowledge, water, crafts/arts and creation) or Prometheus, the Titan who stole fire from the gods and gave it to humanity.
All in all, Lucifer is understood as either a fallen angel or deity. He can be viewed as prideful, a champion of humanity or an embodiment of enlightenment and freedom.