I heard you like Elfen Lied, and anime that aren't positive. Please allow me to recommend you some! :D I'm going to give you a whole bunch, but for the ones I like myself, I'll put them in bold! :)
While they might not be entirely tragic, or have that much of a final miserable touch to them they can be quite sad to watch through or just give you empty feelings, neither positive or negative.
Series that do have some positivitism in them but the negativity is still there, or it turns out later to be rather depressing or scary: Madoka Magica, Blood-C, Another, Ergo Proxy, Jigoku Shoujo, Devilman Crybaby, Mahou Shoujo Site, Mahou Shoujo Ikkusei Keikaku, Shiki, Corpse Party, Higurashi.
If you would like to have some more action in it and it being like the main point of the story; Soukou no Strain, Tokyo Ghoul, Hellsing (it's just an amusing anime, characters are not relatable, they can be just cool), Darker than Black, Fate/Zero, Basilisk.
If you feel like watching a comedy that might have relatable elements, check out Sayonara Zetsubou Sensei and Watamote :)
- I cant promise you that you will like them because obviously I dont know your taste in anime that well, but hearing that you would rather avoid positive animes, it did motivate me to mention some animes that I really liked and others that I didnt like that much and Im aware of how dark they can get, don't be fooled, some just look innocent and nice at first later the proper action begins. Hopefully you will get interested in watching anything from this small list I have made, or maybe you even heard or watched some of them!
If you do like Lain after watching it, keep in mind that there is also a PS1 game that you can play on the browser, that is quite cryptic and provides a different experience compared to what games usually are, and there is a short story Lain manga called The Nightmare Of Fabrication, while it is so short that you cant even get in a mood, just read it shortly after you finish anime or when you play the game, it fits the mood nicely.