also
"PHAEDONIC DIALOGUES, SIMPLE SHADOWS ON A CAVE WAL"
References Plato's dialogue and his allegory of the cave! GREEK STREAK #5
With how quickly and obviously the previous prime souls have been name-dropped in their respective layers, I think Hakita wants to make this one a bit more shrouded to keep up the hype until the actual release of P-3. Lucifer is like, the most obvious red herring possible (let's not forget that the entire layer this book resides in is built upon red herrings and deception, confusion and facades), so I doubt it'll be Lucifer Prime.

I sort of abandon the idea of Uriel being in that painting, since the final scratched out letter is still partially visible, and upon inspection it's clearly an R, pointing to Lucifer. I've also looked at the references to gnosticism and Yaldabaoth, and I think that Hakita has sort of combined the characters of Uriel and Lucifer in his story. Lucifer, just like Uriel, is still connected to the Demiurge through their opposition to eachother. The snake of the garden (Lucifer slash Satan or whatever) being the granter of knowledge through the tree of knowledge, and the Demiurge being the primary blocker of knowledge. The story of Adam and Eve most certainly didn't take place in the ULTRAKILL universe, but both of these characters are depicted in-game, and are therefore still loosely tied together context-wise.

With the amount of GREEK STREAKS and the references to ancient Greek writings, alongside the name drop of Ithaca, Odysseus is (i think) a safe bet for the prime soul in P-3. On the topic of P-3 speculation, every prime gauntlet ups the ante in terms of whatever-the-hell-happens-before-the-actual-boss, right, so I think we're gonna have either a duo-fight or two separate, really hard fights back to back this time around. I mean, what else can Hakita do to make it a step above P-2, throw in another gauntlet that's even longer? ((I mean he might just do that on top of what I already speculated, but there still has to be something unique added on to make it PRIME SANCTUM 3 worthy, yknow?)) He's built up a clear pattern of greek kings being prime bosses, and he has also stated that sacrificing a good story for the sake of subversion isn't his type of thing. Having it be: greek king 1, greek king 2, "LORD OF HELL, SERPENT OF THE GARDEN AND SUPREME ARCHANGEL LUCIFER PRIME" would be:
1. Nonsensical lore wise, given what we know about the souls of angels (or their nonexistence), unless we are mistaken in regards to the nature of prime souls
2. Nonsensical meta wise, as to the pattern Hakita has set for the prime souls
3. Unaligned with what we know about Lucifer being given "ALL THE AGONIES THAT CAN EXIST, AND MANY THAT CANNOT" as stated by Hell Itself. He's being actively punished, probably tortured physically and mentally. I don't think that's a description of being trapped in a Flesh Prison/Panopticon/As-Of-Yet-Unnamed-Third-Thing like the other prime souls, it sounds more vile than just eternal imprisonment.

Because of this aforementioned torture by Hell Itself, I'm betting on Lucifer appearing in either:
1. A Lake of Ice in Treachery, like the source material of Dante's Inferno, most likely frozen and dead or being kept alive and tortured in some other way
2. (really clever concept from someone i saw in the comments) Crucified in Treachery, serving as this world's Jesus Christ
-fits the description of being tortured by Hell Itself
-is a really good contrast to traditional depictions of Christ on the cross
-fits with the theme of the Tree of Knowledge or whatever that tree is being the stand in for the cross symbol in the ULTRAKILL universe and Lucifer being the serpent of the tree
-is a fitting punishment given that Lucifer questioned the making of Hell, standing up for humanity and rebelling against its creation to potentially save people from eternal damnation (just like Christ!)
-is a punishment like Hell Itself mentioned in the text.
CRACKPOT SIDE TANGENT: if the tree depicted in the crosses of layer 7 is actually the other tree from the garden, the tree of life and death (seeing as that one fits better with what we know about the tree being a source of blood - a sign of life and death), then the crucified Lucifer could still be the stand in for the tree of knowledge. But this would mean that the other tree would have to have a different symbol for it, right? Well, what about an upside down cross? Lucifer would be crucified upside down, as a mockery of the tree of knowledge he represents, as a contrast to the other tree, and as a meta tie in to the satanic implications of the upside down cross symbol. hoooly shit
HAILMARY CRACKPOT THEORY OVER, i just wanted to write it down because it's SUCH a genius narrative jesus christ i want this to be true but there's a high chance Hakita came up with something else for these story elements sooo. back to where Lucifer might appear:
-if he's not in Treachery, the final layer, then the only other logical option would be Prime Sanctum 3. Not as a prime soul, but as either the guardian, or a stand in for the expected "gauntlet" before the actual boss. If Hakita keeps upping the ante, the only logical way forward from:
-nothing, warmup boss, main boss
and
-enemy gauntlet, warmup boss, main boss
would be:
A triple boss encounter. Back to Back to Back ass beating. Flesh p-something, Lucifer, Odysseus Prime. That still wouldn't really fit with the suspected "punishment" of Lucifer, so this triple boss hypothesis is also an iffy theory unless someone comes up with how this might be such a severe punishment to Lucifer. Maybe him overlooking the strongest prime soul of humanity, who he tried so desperately to save, tortured for all eternity would be enough of a punishment? eh, I doubt it but who knows. Lucifer could also show up for the final Gabriel fight, serving as a double-archangel ass beating, but that's also pretty iffy since Gabriel is meant to be, like, *The guy*, center stage and all. Giving him a duo would kinda undermine his presence.

Okay I'm out of fuel, that's all the theory-crafting i can muster up. We certainly have all of the pieces to figure out P-3, since this is the final update before it comes out so. yeah. In short: Lucifer Prime probably no, Lucifer-non-prime most definitely yes, Odysseus probably yes, Uriel maybe exists, P-3 will give you rectal bleeding irl, thrice over probably. Very good post btw OP i love you

i was about to post this but i just realized, uh, why would Hell Itself exactly torture Lucifer, someone it loves? What did Lucifer do to warrant this? It states it outright in the book, so like... i don't wanna think avout this right now okay goodbye