Can someone explain to me what the Dream World introduced in LoLK is? I don't get how it relates to the plot, why the Lunarians had to go there, or what it even does, frankly.
(hope this is the right place to ask...wasn't quite sure, don't want to cause a hassle for the mods)
Uh, the Dream World is fairly new and there aren't too many explanations about it, but let's try anyway :
Can someone explain to me what the Dream World introduced in LoLK is? (...) or what it even does
Even if LoLK introduced it, I think WaHH gave the most explanations regarding Dream World related stuff. If I understood correctly, things goes more or less like this : when people sleep and dream, their consciousness (or soul?) goes on a trip to another reality : the experience it lives there is basically what a "dream" is ; and in order to get to that dream, the consciousness (or soul?) of the dreamer passes through the Dream World : in other words, the Dream World is essentially some sort of passageway that binds differents worlds / places / realities together. Sort of. For example, Sumireko can access Gensokyo through her dreams.
As for LoLK, in order to get to the Moon, the heroines used a certain passageway that brought them in the Dream World physically. Here, the Dream World might seem like it's just some random place that they happened to pass by in order to solve the incident, and might therefore seem irrelevant ; but its relevance is mainly because of how it is tied to Sagume's plan :
How it relates to the plot
The plot being mainly about Sagume's plan, the Dream World is obviously not the focus of the story. But it does hold a certain relevance toward Sagume's plan, and the plan's point is basically how to get the Lunarians out of the mess they are in :
Why the Lunarians had to go there, or what it even does, frankly.
Junko's invasion was basically about flooding the Moon with "impurity" / lifeforce and render the "pure" Moonies unable to react. "Impurity" here is mainly about life and death : if it's alive, it can die. But here's the thing : the "pure" Lunarians are able to enjoy extremely long lives because they reject the notions of "life" and "death" : if it's not alive it can't die (so, basically, they're amortals). So, if the Lunarians were affected by the impurity, what would happen ? They'll become mortals, and that is not certainly not the first thing on their wishlist. So, basically, the Lunarians had to move to the Dream World because the Lunar Capital was threatened by a massive amount of impurity.
Now then, back to how the Dream World is related to the plot : Since the Moonies were unable to do anything against this threat, obviously, getting people who had no trouble whatsoever with impurity deal with their problem was the obvious choice... and these people had to somehow end up in the Moon, say, for instance, through the Dream World. Besides, the heroines getting in the Moon conveniently to deal with their problem seems reeeaaaaaaaally suspicious, I mean, the Moonies have shown in CiLR that they are able to with whatever way outsiders might have to intrude the Moon, so...
So yeah, all in all, the Dream World is essentially an important piece of the puzzle that is Sagume's plan, but certainly not the focus of the story. There might certainly be other ways to highlight its relevance, but IMO, it's minor compared to the Lunarians's scheme.