TL;DR: Lain showed (perhaps, unintentionally) Alice near-everything she had seen on the Wired, all at once
What (physically) happened in Lain's room in that scene doesn't seem to make any sense, no matter how I look at it. Symbolically, it seems like Alice got somehow connected to the Wired in a way akin to Lain herself, and her mind failed under the overflow of information.
A lot of Lain is reflections of contemporary rumors, worries, and fears about the internet. Even now, trying to grasp its immense complexity makes it seem like some unknowable lovecraftian abomination. I imagine facing it directly, not throttled by one's ability to physically perceive data, would be devastating.