In a general respect, representing Lucifer and Satan as the same is a gross fallacy, imo. Representing Lucifer as a single individual would also be a gross misrepresentation, as I see Lucifer as the principle of small realizations and understandings that can lead to the beginning of great transformations. Similarly, representing Satan as a single individual would also be a gross misrepresentation, as we can all unconsciously project that which we don't like about ourselves onto others in Jungian Shadow projection. {This principle of no single individual representing the archetype can also be seen in the Christian paradigm of there not being a single individual called Antichrist, but rather, there are many Antichrists. (1 John 2:18, 2 John 1:7) I personally see the spirit of Antichrist as a collective consciousness that has been infected/poisoned by greed, hatred, or delusion, that can infect several individuals all at once and overcome their minds to they do unchristian things like lie, steal, kill, harm others, persecute others, take other people's spouses, and tell others to do the same.}
Your mileage may vary.