Things to note:
I’m aware the name Lucifer is only mentioned once in the bible.
I’m aware Baphomet has a muddled background between the Egyptians, Templars, etc,.
I AM NOT ASKING ABOUT BAPHOMETS’ EXISTANCE. He is quite real from my own experiences.
My question is: are the three considered different entities or is Satan and Baphomet different masks of Lucifer?
well i am not sure about baphomet. even tho baphomet comes from the arabic word FHM which means understanding.
To answer your questions: Lucifer and satan are the same but not the same. 
i know i know its confusing.
Lets say they are the same but not in terms of different masks >> thats the closest way for me to describe it.I hope it answers ur question
As mentioned so many times in the forum already, these three beings are different.
what! i thought satan and lucifer are one but different masks!! are you sure?
How I see it Satan is the God and Lucifer is the Emperor…I maybe wrong but I think they are two different beings
They’re not different masks at all. They’re completely different beings.
Now, Satan is a being made of parts of other spirits (like Lucifer), but he has his own parts too. This has also been said by Lucifer and Satan themselves (you can find more info on that in the forum, we have lots of threads for this matter).
I mean, it’s a way to see it. Lucifer is known as the emperor and Satan as a great godlike being, so, it’s not wrong to assume that.
i see.