Wow that was a ton to read, but pretty nice all around.
Okay so:
I'm guessing Living Weapons are former parasites.
Judging based on the theory that the trinity is just high level parasites and hosts, I'd guess that they never lost their status like the others.
Double is probably the missing half of Lamia's face. As they regularly reference Christianity, it'd make sense that Double was made in "Lamia's image". That would make her not only the double of others, but also Lamia's double given how the cathedral stained glass of Lamia has vague similarities to human Double.
(Blonde hair, female...Again, vague)
How she bears the grudge is also in line with her winquote: "I am merely an instrument of her will." Makes sense given how she became uncharacteristically angry in this loop. I'm guessing death is either a minor setback or just of the Venus or Aeon of that timeline.
In any case, if the trinity are just parasite users, I'm guessing the crown itself is the parasite in Lamia's case.
I'm hoping Ms. Fortune somehow helps Filia and Squigly escape and the three of them attack Eliza if Marie doesn't win. I'd assume Lamia cut a deal with Marie: If she kills Eliza, she can be rid of the Medicis.
If that doesn't work, there's...
And if none of those work...Beowulf will be here before long.
Sidenote: The left side facial covering seems to recur alot, even Nancy has it. Is it meaningful or just coincidence...?
(The fallen head of Lamia has half her face covered too)
EDIT: So I forgot to mention. Is Eliza just a guise Sekhmet takes? Because literally it seemed like it was all Sekhmet the entire story. I didn't see "Eliza" express individuality or anything that would imply she isn't just a skin that her Parasite is wearing.