First, when Lain unflinchingly approaches the gun-weaving stoner in the club, and tells him "No matter where you are, we're all connected". The guy then turns his gun around, shoots himself, and Lain gets all splattered in his blood. Massive awesomeness for a quiet 15-year-old little girl, and sets the grim, disturbing tone of the rest of the series.
The Latin American dub is even more awesome: she says "Nobody will escape, not even you, once everyone's connected".
How is that awesome? This troper found that to be the creepiest thing to that point! She up and murdered someone, after apparently using him to murder someone else, and didn't even seem to be aware she was doing it!
Then, at the very end of the series, Lain tells "God" that he's just a sicko scientist who thinks he's the best just because he uploaded his mind into the Wired. Then he materializes himself into Lain's bedroom with Alice next to her. Lain then holds Alice real tight, and telekinetically throws him all the stuff piled in her bedroom, effectively killing him for good.
Lain's Berserk Button gives her telekinetic powers. She melts a building out of pure despair. A guy almost got his face taken off for staring into her bedroom. A god upset Lain's best friend once. Once.