Whether it's the adversary or the accuser, it's not really important. In Judaism, it's a human inclination toward evil. In Christianity, it's subjugated to God; one's Christian life begins with an exorcism or a renunciation of Satan in baptism, at which point we move beyond it and stop blaming it for our own failings.
Satan/the devil is not Lucifer though. That's a Latin calque of the Greek Eosphoros, from the Septuagint, translating Hebrew Helel. It's just the morning star, i. e. Venus. It might have been a Semitic deity at one point, the b'nai Elohim were the stars, but in the Bible it's applied to a Babylonian king. The writer is mocking him; Babylonian kings would "ascend to heaven" and take on the role of a divinity in their religious rites, but like all humans, they would eventually descend to the grave. It's not a reference to the satan.