Satan is a personification of the Judaic word ha‑satan meaning Adversary. Ha satan did not become Satan until much later when Jewish sects / tribes particularly the Essenes began referring to anyone who was not an Essene as ha satan. Still further on, the Roman Christian Church decided it was time to personify "the adversary" into Satan (complete with horns, tail, colored red, and all that jazz) and have him become the scapegoat for all evil in the Christian world.
Lucifer has nothing to do with the Abrahamic faiths, he is NOT the Satan found in the Abrahamic myths. Lucifer as a deity is not mentioned in the Christian bible, but the word 'Lucifer' is used adjectivally as a title. The biblical use of the word Lucifer is personifying the Morning Star of Phoenician/Canaan cosmology.
Lucifer the Roman-Greco deity is mentioned in Publius Ovidius Naso's "Metamorphoses", which was written in 8 B.C.E., the Roman poet Virgil mentions him as far back as 29 B.C.E. And the first mention is from Timaeus by Plato in 360 B.C.E. This Lucifer is also portrayed as a Lunar deity unlike his usual association with Venus.