The identification of “Lucifer” with Satan probably began with St. Jerome and his Latin translation of the Bible. I got this by skimming the Wikipedia article on Lucifer, which I recommend. So your suggestion seems to me ahistorical. Also note that Jesus is referred to as the Morning Star in the NT.
I was actually going to address that after my most recent post. I consider, based upon research, Satan and Lucifer to be two distinct beings. So thanks for the chance for me to segue into that.
The word "Lucifer" in the original language means light bearer. Isa 14:12 How art thou fallen from heaven, O Lucifer, son of the morning! [how] art thou cut down to the ground, which didst weaken the nations!