Well, I don't know if it was already discussed, but there's few things i noticed.
First, some issues that may be involved here:
1) Where's Rei 2
2) What is 12th Angel and how it got into Mk6
3) Why Lilith's head looks like Rei\Yui
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So, in 2.0 Rei was devoured by Zeruel and somehow ended up in its core:

Note, that Rei also says something like "now this is the only place I can live in". Is she talking about core?
Now, we see giant naked red Rei, that red substance definitely reminds angels'\evas' core material.
Giant red Rei merges with Eva-01 core.

Now, in Q we can see 12th Angel, which was sealed in Mark 6 and known to be purely core thing, transforms into giant Rei head.

Again, big red Rei made of core.
Ok, what does it all mean?
Could it be that:
1) Red core-ish Rei (or part of her) was transplanted into Mk.6 (is this what Kaworu was referring when he said Mk.6 was turned into autonomous state?)
2) Then somehow became 12th Angel, or was merged with\infected by 12th Angel and
3) Made contact with Lilith and this is how Rei image ended up in Lilith.
Or somehow she just broke free from Unit-01 and became an angel.
Or 12th was a different thing, but it took control over Mk.6, which had core Rei as part of control system, as said above.
Also, notice how all those FOI-evas are red.
Fuyutsuki's word about Rei being inside Eva 01 can be explained like that:
1) He's lying
2) Rei was split into two parts or something
3) He's talking about her soul, and red corelike body was used in some different way
Just wanted to share my thoughts.