Malika: Makes sense to me*. The DA had Chaplains pretty much wholesale, they might've found a lot in common with whichever Word Bearer representatives were tasked.
Spotting an 'in' on the Legion, the Word Bearer appeals to Caliban's now disappeared knightly orders - "Wouldn't it be nice to honour the past with this as a mechanism for ensuring the Legion works at its very best?". A few trial runs within the local chapters, all of a sudden the DA's unnoticed disposition for 'secret clubs and circles within circles' runs riot and the Word Bearer's quickly lose any control! There's the 'Secret Society', nod nod, wink wink, which is actually just a 'down time forum' for the bulk of the Legion to exchange ideas in a slightly less formal, but not completely informal way.
Nevertheless, as soon as that starts, some smaller order of that group think "Hey, we could use this really well for getting one-up over <rival chapter>! Keep it schtum from the rest of the Chapter, but if you, you, you and you do this...". Meanwhile everyone's doing it.
The emergent property would be that the Lodges would institute themselves well within the legion, yet they'd also be almost completely ineffectual compared to, say, that of the Sons of Horus or the Death Guard - the DA Lodges ('orders') quickly take control of their own destinies. Unfortunately for them, some are stronger than others (e.g. Deathwing) and they start becoming dominant forces within the legion.
To that extent, like After Desh'ea, Deathwing mightn't be the pre-eminent of these organisations during the Horus Heresy, rather they'd be more akin to Captai Kharn of the Ninth Company - the only ones standing with any sort of command perspective of know-how to actually cover up the mess that'd been made. (Or did they? Perhaps the Deathwing didn't really seize control until much later, having ejected previous dominants?)
Unfortunately, as noted in the 'Primarch Discovery Orders', whilst there's a certain 'intellectual allure' to all of this, one has to measure it against when it stops being useful to story-telling. (As you can see from the brackets above: this would happen very quickly indeed, if you're not careful!)
But, critically, if it's not mentioned at all, it still remains a massive 'oooh, what if?' potential twist. What if, for example, it's Deathwing who side with Luther, and the whole myth-structure is co-opted by the post-Heresy Dark Angels for convenience because the Deathwing were 'somewhat' known to outsiders... it was just easier to internally re-brand than come up with an even more complex lie to tell everyone else?
My head hurts!
* Thinking on it, as weapons go, could the Lodges have been scatter-fire? Would they really have only been used in the Death Guard, Sons of Horus and Emperor's Children? Perhaps they only needed, say, a 33% success rate to be 'worthwhile', so the WB's tried applying it to, say, the Space Wolves, White Scars and Dark Angels... but in each case, the Legion's own personalities took it aboard a little to seriously, perhaps, or had already instated a 'better system'!