In 1.11 and 2.22, Seele speaks of a Covenant with Lilith, and how she will be resurrected in accordance with the awakening of the True Evangelion once "the necessary rites are carried out." On its face, this seems to refer to the soon to be completed Mark 06, and the horrible Mk6/12th Angel/Lilith amalgamation and Lilith's apparent death in Central Dogma suggests this happened and failed with the aborted Third Impact.
You'd think Lilith dying would turn all their plans ass-up since that was being pitched as part of the end-game, but as Seele tells Gendo as they're being shut down, they have everything they wanted and all went according to plan. That whole situation in Central Dogma and how the heck it happened has given me huge migraines trying to make sense out of it, but it got me thinking
When the 12th Angel expands into the giant core, it dips into Lilith's LCL/blood and begins to take on the shape of Lilith's giant rotting Rei head, but red, and then it begins to bloat into a giant fetus shape, which seems to signify a birth. Or perhaps a rebirth, like Lilith is reforming herself in an embryonic state, like Adam did in the original second impact. And while that giant baby-thing is forming, Evangelion 13 starts to wake up, matching with Seele's goal earlier.
Eva 13 eats the core and takes on a form that's wildly different from Unit 01's in just about every regard and different from the Adams we see at Second Impact: it's white, has red eyes and looks very solid as opposed to their wispy burning look. Unit 01 was becoming an energy form while Eva 13 is just glowing.
Now that could probably be attributed to the two Lances and the presence of two pilots, but I had another idea: what if the revival of Lilith and the awakening of the Eva aren't just two events that happen concurrently? but are actually the same thing. Mari guesses it's an Adam(s), but could it be that Eva 13 is actually intended as a vessel to revive Lilith, almost a reversal of what happened to her in End of Evangelion?
It does match the colors we've seen from her previously: glowing white body with glowing red eyes. And if you look at the scene where she spreads her wings during Third Impact, the pair of wings jutting straight up out of her shoulders look somewhat similar to Eva 13's wing-like pylon growths, albeit without the actual bone/wing structure:
SPOILER: Show
And right after it powers up, the first thing Eva 13 does is rip the Black Moon out of the ground and seems to be exerting some kind of control over it, making it fly and activating the undulating corkscrew ridges along the sides. On top of that, the inert Red Evas, which were drawn to Lilith's corpse before, are drawn up into the vortex of debris and are flopping around while making sounds. If Eva 13 is just one of the Adams, how and why would it uproot the Black Moon, and why does it only seem to effect this and New Nerv HQ but nothing else that we can see?
Kaworu says it all happened because Gendo tricked him and turned him into the 13th Angel, and this is another bug in the ointment. We don't know what that means or why it's a big deal. He was already an Angel before and he piloted the Mark 06 and Eva 13, both Adams, with no problem whatsoever. Nothing happened until 13 ate the 12th Angel.
Here's what I'm thinking: whatever this change was, it forced him to become a proper Blue Pattern, which he evidently was not before. He didn't show up on any of the equipment in Units 02, 08 or 13 until after the change happened. He was inert or something else before, and the ritual forced him down from that status to a mere Angel. I can't begin to guess at the mechanism here.
Misato told Shinji in 1.0 that if an Angel made it to Lilith, it would trigger an impact. Gendo gets to have his cake and eat it too: The final Angel, the 12th, is killed, fulfilling a part of the bargain as stated by Seele. The True Evangelion is awakened, Lilith is revived in a form under Gendo's control, but he still has an Angel that lets him trigger an Impact to free the Black Moon from beneath the Earth but cannot stop the Eva because Shinji is keeping it awake. And said Angel cannot stop the Impact thanks to Shinji is handily dealt with courtesy of Wille.
And it also opened the Doors of Guf, allowing Fuyutsuki and Gendo to fly their pyramid inside, if that's what they did. You can see it hanging under Eva 13 as it spears itself, but it disappears after that:
SPOILER: Show
That would be one hell of a coup on Gendo's part!
Related to this, I believe Kaworu was mistaken when he said the Mark 06 was remodeled into an autonomous unit. Rather, I think he was lead to believe so and it was actually being piloted by one of the Ayanami-series when it was infected and merged with Lilith, which is why is why Lilith took on the Rei shape. The only other method I can think of is that Unit 01 was somehow at the scene when it happened, but it's hard to justify Unit 01, Mark 06 and the 12th Angel all three being there and Unit 01 somehow being removed after the fact.
That's the gist of my hypothesis! The new mechanics in 3.0 are so obscure and convoluted that it's really hard to fit all the facts into the scenario. Especially since our chief narrator, Kaworu, might be wrong himself!