Based on that one statement during the fanfest Koji made about the "sudden appearance" of the crystal tower in lake land, I'd like to take a wild guess as to the crystal tower's origin on the first and say that it is in fact the same CT from the Source.
To partially quote a post Moose made in another thread, the possibility of temporal displacement and CT existing in both areas at once, I'd like to take it one step further and speculate that in this case it's likely to be fully fledged time travel.
Mr. Not Graha made pains to express to us how unimportant our war with Garlemald was compared to the greater threat the light of the first poses to the world at large. He clearly knows the events that have taken place up to the point of the war all the way to the "twin dooms" calamity to some degree.

This is my guess, after the events of the CT raid, Graha awakens from his sleep to find the source(well everything really) in some near complete cataclysmic destruction, uses the crystal tower to look into the past to find a suitable point in time intervene and avert this calamity and enlist the aid of the only people who have the potential to change the events to come.

This theory aside I can't help but wonder how much the ascians know about what's to come? Is this twin doom something even they don't foresee? Is this all part of Elidibus' plan and we're just playing right into it? The must know SOMETHING since Solus made refrence to the spreading light of the first having some sort of "effect" on the black rose gas in the source and maybe that plays a part of the "twin" doom aspect.

It's all just speculation for me what do you all think?