Welcome to the "Lilium Project"

But yeah I just watched it front to finish a few days ago and am just captivated by it, best I have ever seen even with the weird ending...Anyone ever want to debate/talk about this sucker I am allears for it! Kept me up all night last night thinking about that crazyending!

1. I'm going to have to agree with some of the others, the clockrepresents Nyu, the lilium music box represents "Lucy", or Nyu when shehad all those problems and was troubled about what she did to Kouta.Obviously they aren't going to cut straight to the music box and theclock while their conversation was going on the steps, but the writerssaw it best to throw it in at the end to give the story more closure.

Nyu has made atonement for the hurt she carried around her whole lifefor Kouta and has moved on in life, no longer bitter against humanityand no longer oppresed by humanity to the point that she becomesdesperate and believes she does not even have a place on the earth andthat she is not even human...

2. I came up with two very probable conclusions concerning the personat the door, firstly...I don't think that "Lucy" died, I think that Nyusurvived and has moved on from her past self, as I said above...

On the other hand, remember what the Chief, Kakuzawa said toArakawa..."Tell them to do what is necessary as long as they bring backher head and torso!", and "My plans for you have just begun!" rightafter revealing his secret...

So maybe it was Arakawa? Maybe lucy got shot down but the teams thatwere sent to get her captured her head and torso, and somehow Kakuzawaput her parts into Arakawa to make a replacement? Or maybe it was Lucyrunning away as they tried to capture her?

They went into episode 13 with plans to continue the show clearly, thatis obvious, but I think that due to the shows failing popularity at thetime ( I mean come on!!! Its rated NUMBER 6 Now XD!!!) They ran out ofpatience and funds and had to come up with a quick solution, so theyended it happily but left it open still for more material just in case?

No matter how you look at it, it was a awesomely done Anime, I hatedevery page of the manga personally, especially that horrible ending(Thereincarnated twins was a nice spin though!) The Anime is far thesuperior IMO, but since they both wound up going seperate ways(And boyo' boy did they! Totally different storys, with the manga be extremelyfar fetched and predictable I might add IMO!!!!!) It is like they justlost hope :/ I would eat up a new season, these guys are geniuses!!!!!

More than likely though they had to rush to end, so they gave it a nice ending with blantant symbolism to figure it out, It is neither Lucy or Nyu. Lucy is the name generally given to her when she was just a lab rat, tortured and twisted by everything in her entire life and tortured by her actions in the past to the point of insanity. Nyu was a personality disorder resulting from severe head trauma and extreme terror of having to face down her past with Kouta. The person survives but is over their past, name them whatever you want.

Are you aware of the manga's plot line after the anime ends?  If not I'll fill you in.  The anime's plot diverged from the "real" story at around episode 11 IIRC.  The "real" story, from what I've read and heard has a much "worse" ending.  I don't think it has been 100% scanlated yet, it's sort of in a quagmire somewhere around the last few chapters and they just haven't been translated for some reason.

Anyway, the reason this happened is that the anime ran out of material, such as happens frequently.  Anime productions will usually either end prematurely with an original ending based on what the anime staff thinks might happen (Elfen Lied), or they announce a second season for a later date (Haruhi), or they just piss everyone off and make low-budget filler (Bleach/Naruto).

Personally I'm happy with the ending the anime staff came up with, I've seen a lot worse.  I'm all but certain that the person at the door in the end is intended to be Lucy.  I would guess that she finally resolved to stay alive, but realized that she would be putting everyone in danger if she did so without first putting an end to the evil organization.  One way or another, all the bad characters are no longer a threat, or she wouldn't have returned.

If you zoom in on the person at the gate, there can be no mistake, it is clearly a woman, and a very tired or injured one at that.  There are no other signficant female characters in the story who are unaccounted for, and not even the most crazy anime staff would use the last 10 seconds to introduce a completely original, unnamed, unseen person.

My guess is that the anime staff wanted to give the show a happy ending, after all the horrible things that happen in it, but they couldn't be 100% clear about it for one reason or another.  Anime, or rather, Japenese authors in general seem to enjoy leaving a somewhat-ambiguous ending on a story rather than a "Hollywood" ending where every last thing is sorted out.

I'm relieved happy that, even in a "fake" ending for a fictional story, Lucy finally gets some peace and happiness.