As I learned, there is no one and only truth behind Lain. If you ask me:"How does Lain ends?", I can only say that Lain never ends, it only begins. The story that follows, is put together from all the fragments printed on the videos. It summarizes the Lain story, without giving away any spoilers

It sounds very WEIRD, but it's fact.
Mail comes from a GIRL
Who has never been here.
She speaks to you that
"Why don't you come over here soon"
PSYCHE, leads lain to WIRED,
another world beyond network,
Where any sex, age, nationality
and RELIGION here means nothing.
WIRED has been supposed to
support for the REAL WORLD
But something is going on
to change how two worlds have been
and it cause lots of DISTORTION there
It needs KIDS
because they are the future.
It is full of RUMORS
which are there
al long as people live
that is SOCIETY
Words and body in REAL WORLD
and device and PROTOCOL
in WIRED have enabled you
to communicate LOVE with someone
BUT it seems to be changing
See INFORNOGRAPHY
and you will know
the bind between WIRED
and REAL WORLD is about to
be broken because of one girl
These two worlds will become united
and we need no more device
to connect to WIRED
How do you think?
Will there be any change in your LOVE
What can you see?
A house stands behind you a slope in front of you
wires above you
Now how do you look like?
that is your own LANDSCAPE
which is the reflection of your EGO