At the basic level we accept our senses as truth. Our experience of the world is indeed how the world is. This is how most of humanity goes about their daily lives, in the Matrix as it were.
Then with some thought it becomes obvious that the world of our senses is not the reality of the world. Plunged into this frightening new reality, things that you took for granted your whole life are now uncertain. Really, if the senses aren't The Truth then how do we establish The Truth? Is there a Truth out there to know? Are there many Truths that depend on each of us individually? All these possibilities blossom outward from this fundamental realization.
This is the level at which Lain exists. In the Wikipedia article it specifically mentions how the authors were very pointed in making sure there was no God view of the situation. Indeed, that they actively encouraged the ambiguity on whether the Wired or the "Real" world was superior. They also pursued the idea that it was uncertain whether it was reality that gave rise to thoughts or if thoughts gave rise to reality. It is the ultimate house of mirrors in which you can never be sure if what you're looking at is the real thing or only an illusion.
But there are stages beyond this. Kant exemplifies this in Western thought, although his particular brand isn't the only version in town. One of the best phrases for illustrating this idea is a Buddhist phrase: "Things are not as they appear, nor are they otherwise." In this stage the uncertainty of the senses is still taken for granted, but two key aspects are recognized:
a) There is not an arbitrary relationship between experience and reality. There is a correlation but not a correspondence.
b) It isn't that we have the wrong "view" of reality. It's that reality is "unviewable."
The first is important because it begins to address some of the rampant relativism that sprung up with the first dethroning of the senses. Yes, the world is not like what you first thought, but that doesn't mean it is every which way either. The second is key because it is coming to an appreciation of the limitations of human conceptualization. It isn't that what we conceptualize creates reality, it's that what we conceptualize is the way in which we bound it. These details relate to certain key aspects of reality, but they are not, in fact, representative of it.
The best metaphor here is again a computer. Look at your monitor. You likely have several windows open. If I were to ask you which window was on top you could easily point to a particular window that was over all the others. But you would be wrong. There is no such thing as "on top of" for the window because it is a 2D screen. And it is nonsensical to talk about code being "on top of" other code. The properties of being "on top" for the window DO mean something for how you interact with it (when you click your mouse what happens, how it interacts with other windows, etc.) but being "on top of" is not an actual computer reality. To ask which is on top is to ask a question which has no answer, for you have framed the question improperly.
I have some suspicion that there are yet more subtle and developed understandings that exist, but (for now) they escape me. What I describe above is the current limit of my development. So when I look at Lain I see a stage which I have passed through, which I appreciate as valid but simultaneously one which is no longer fruitful for me to contemplate. This is why I didn't say it was "wrong" like the existential section. It's not that it's proven wrong, simply that I regard it as a more formative vision.