You know, i was thinking about it. And I'm starting to think that LoD DOES = CO.
My reason behind this is that Nomura said the Chamber of Waking existed BEFORE CO did.
We've seen the inside of the CoW and it's littered with Eraqus' insignia.
Which means, the Chamber could have been in LoD for a while, and then, LoD became CO.
That'd at least explain how the CoW could exist before CO did...