You wanted mindfuck - you get mindfuck. If you do not understand what Lain is about the first time you see it: don't worry. You really have to constantly watch for clues and think about what you have seen or else you won't be able to make any sense out of it - and thus won't be able to enjoy it, because you won't be served cool action scenes to distract you from thinking.
This is - by the way - one of the first animes I have ever seen consciously (seeing Heidi or Captain Future as a kid doesn't count) and thus got a rather warped impression of what anime is about. ^_^
Following are a short plot description and a more elaborate - er - elaboration taken from IMDB and wikipedia.
Enjoy !
PS: Safe for all ages but if your kids understand and like Lain then start worrying.
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A week after Chisa committed suicide, her classmates begin to receive emails from her. Hearing rumors fly at school, a quiet withdrawn girl named Lain goes home that day, turns on her dusty Navi computer for the first time and has a conversation with the dead girl. Chisa's message reads that she killed herself because she didn't need her body anymore, and she now exists in The Wired. When Lain asks why someone would do something like that she gets a response: "Because God is here". --- IMDB
Serial Experiments Lain deals directly with the definition of reality, which makes its complex plot difficult to summarize. The story is primarily based on the assumption that everything flows from human thought, memory, and consciousness. Therefore, events on screen can be considered hallucinations of Lain, of other protagonists, or of Lain fabricating the hallucinations of others.
Story misdirection is central to the plotline; even the offscreen voices or narrations' information cannot be considered truthful. The series consists of a cross-reflection of philosophical themes instead of the traditional linear events depiction: episodes are called "layers".
Serial Experiments Lain describes "the Wired" as the sum of human communication networks, created with the telegraph and telephone services, and expanded with the Internet and subsequent networks. The anime assumes that the Wired could be linked to a system that enables unconscious communication between people and machines without physical interface.
The storyline introduces such a system with the Schumann resonance, a property of the Earth's magnetic field that theoretically allows for unhindered long distance communications. If such a link was created, the network would become equivalent to Reality as the general consensus of all perceptions and knowledge (see consensus reality). The thin line between what is real and what is possible would then begin to blur.
--- Wikipedia