Darth Darth Binks
For this theory, I am disregarding the fanmade ending (even though it's right)), as well as the statement that the creators made about him being dead. There are many ways to translate what he said, especially over the language barrier. Needless to say, SPOILERS!
To determine if he is alive, we must first find how the Code gets passed on. CC gets her Code when the nun fatally wounds them both with a sharp object of some sort. Both were "dead" when the Code transferred, and then the nun truly did die. When Emperor Charles gained his Code, he was ordered by Lelouch via Geass to shoot himself. A fatal wound. We know that before this, VV is bleeding to "death" outside that cryptic door. When Charles shot himself, both he and VV were now "dead" and the Code was transferred, and VV truly died. We know Charles could not have had his Code when Lelouch first confronted him because Lelouch's Geass worked on him.
We know now that the Code gets transferred when both a Code bearer and a Geass user are "dead." We could also assume that only Geass users with both eyes affected can obtain the Code, but that is not truly relevant.
I will refute the theory that Lelouch gained Charles' Code when Charles had him in a stranglehold with his tattooed hand, because it was not nearly long enough to kill Lelouch. Charles was then wiped from existence. That's pretty dead. Of course, this happened in C's World, which means the essence of Charles and the Code can still be lingering, for it is more accurate to say Charles was absorbed by C's World. Nevertheless, he no longer exists. Because of this, Charles is still "dead" when Lelouch gets stabbed in the final episode by Zerozaku. Because both are "dead" at the time, the Code gets transferred from Charles' essence to Lelouch.
To back this up, Nunnally grabs Lelouch's hand and sees his meeting with Zerozaku about the Zero Requiem, and all that Lelouch planned. A similar occurrence happened between Suzaku, Lelouch, and CC when she is touched by Lelouch in that one episode I can't find at the moment.
Some say that this is only because Nunnally can sense things with her hands because she's been blind for so long. Bullshit. She legitimately saw Lelouch's past. That is not natural.
And finally, when we see CC riding in the wagon cart, she says that she might have been wrong about Geass leading to a life of solitude. And then she asks Lelouch's opinion on it, as she bends her neck back as if she means to talk to the cart driver. Some say she is only looking to the sky and talking to his dead self, but she's already looking upward because she's laying on her back. Why, then, would she move her head if not to talk to the cart driver?
There you go. Lelouch is the cart driver. Rather, Lelouch has died, and is reborn as LL, or RR, as the names of the seasons suggest. The best part about it, is that Lelouch didn't even know he would live. He truly wanted to die because of the guilt of doing so much sh*t to the world. The creators left the driver's face unseen because they ultimately want us, the viewers, to choose our own ending. For me, the evidence is there. What do you think?