(For the sake of convenience, I will simply refer to the 'Lelouch-is-alive!' theorists as the Cartdriver Club for the duration of this explanation.)
The sole foundation that the Cartdriver Club bases the legitimacy of its theories on is the claim that the creators of Code Geass stated that they intended for the viewers to decide what happened to Lelouch in the end.
This claim is not true.
The confusion arises from something said by Okouchi which the Cartdriver Club has taken and grossly twisted to fit their wishes. They took a single sentence, isolated it, and gave it a false context. What you REALLY have to do in order to understand what Okouchi is saying in his quote is to read the WHOLE section of the interview -not just one sentence- or you'll come off with the wrong idea.
What was said was that the TONE of the ending -not the events of the ending itself- is up for viewers to decide. Did you feel that the ending was happy or sad? Good or bad? (IE., Was the ending to
Romeo and Juliet happy or sad?)
Tone, not events. They did not say that they left the end ambiguous.
For the sake of everyone's clarification, here is the interview in question. Do note that they are talking about
how they the cast were
'feeling' about the ending and mention nothing of events. Anyone who understands the English language should be able to ascertain through context clues that Okouchi was not leaving the ending ambiguous.
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Sakurai x Taniguchi x Fu-kuyama Interview, NewType November 2008
--Congratulations on the completion of "Code Geass". When did the thought "It's ended" first occur to you, Director Taniguchi?
Taniguchi: That's a difficult question. Visually, that would be after the V-edit (Video Editing) ended, because after that you can no longer do anything about it. However, in terms of the end [of Code Geass] as a project, I really don't know.
--How did the final recording session go?
Taniguchi: It was difficult for me to control myself, psychologically. Since it was the final recording session, I kept thinking "This is the end", but in terms of the actual work, I had to hold on for a little while longer.
Fu-kuyama: I was thinking "Let's record our lines in high spirits!", but that only lasted until episode 24. The final recording session was...... This might be the first out of all my works so far in which I completed the final episode without putting too much effort into it. I took it all calmly.
Sakurai: I was in a spiritual state of nothingness. More than two years have passed between the recording of the first episode and the final episode. To be involved in a project for so long is something of a rarity these days, and because of that I was also overwhelmed with feelings. Still, "Code Geass", true to its nature, ended in a cool way.
Fu-kuyama: I think the VA with the most mixed feelings when it comes to the last episode of Code Geass might very well be Hoshi Souichirou, Gino's VA. To tell you the truth, I received a phone call on the night before the recording for the final episode. I wondered who it was... and it turned out to be Hoshi-san.
Sakurai: He called me, too.
Fu-kuyama: When I answered the call, all he said was "Tomorrow's the final episode, isn't it... do your best*." (laugh) [*ganbattene]
Sakurai: He said "Do your best" to me, too. I guess he was especially attached to this show.
Taniguchi: (laugh) It's up to everyone how they want to interpret the ending, I don't mind, but for me, it was a Happy Ending.
Fu-kuyama: I, too, think it was a happier ending than expected.
Sakurai: As for me... I'm looking at things from the viewpoint of Suzaku's VA, of course, but I've been watching the show as just another audience, too. That might be why the ending was painful for me.
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That's it. That's where it ALL came from. Do you see anything about open endings in there? I sure don't. I see a bunch of cast members talking about
how they felt.
Now that we have that mess squared away, continue on to
part 2 if you really need to be inundated with further proof.