I'd guess that the reason Lain kills herself in the Wired is part of her trying to make sure that she's herself. As long as Lain of the Wired exists, Lain can't really be Lain. Of course, if Lain of the Wired has and always will exist in the Wired, then killing her won't do anything. By that logic, if there is no Lain in the real world, then that makes Lain of the Wired the real Lain. It's a sad, confused attempt at finding herself.
And yes, it's safe to say that we all love Lain and want to tell her it's okay. Arisu/Alice was able to do that in the anime, but Lain didn't really have anyone to do that for her in the game, which probably explains the difference in tone in the end. [spoiler:lit]Plus, second base.[/spoiler:lit]