Do you think they are the same God? I know the answer, but I want you to tell me.
Unfortunately my friend, I was born and raised a Buddhist. Which means that I am non-theistic. Which basically means that the concept of a God or gods is/are not relevant to my paradigm and world-model. Whether or not Lucifer and Jesus were the same god or different gods or ever existed is a question for the Westerner born and bred inside of a Judeo-Christian culture and society. Therefore: I have no opinions or beliefs regarding your question.
But, I can tell you a few interesting things about Lucifer and Jesus.
1. Luciferi was originally the ancient Latin word for the planet Venus.
2. Every 40 years, in the earth's sky, Venus/Luciferi traces a pentagram.
3. Venus is the brightest star in our sky.
4. Venus is called the Morning Star as well as the Evening Star.
5. Jesus, in Revelation 22.6 says, "I am the root and the descendant of David, the bright
morning star.”
6. Jesus calling himself the morning star is not original. Since the ancient pharaohs of Egypt also had the title of "Morning Star," as did the ancient Kings of Sumer.
7. In that light, when Christ called himself the descendant of King David, and the Morning Star, he was affirming his divine Kingship, just as David was a divine king, made such by Yahweh Elohim, just as the ancient Pharaohs and Kings of Sumer were God-Kings or divine kings.