When I was just searching for theories for why people believe Lelouch is still alive, I found a theory which says Lelouch took the Geass from his dad, so when he was killed he actually became immortal. But on re-watching the series I can't find any such scene where we see Lelouch taking the Code from his dad. Or did I miss something?
When I watched the anime for the first time, I remember it had extra scenes like Lelouch driving the cart, which wasn't present when I re-watched the series. I read that it was removed later.
So, did the writers remove the scene in which Lelouch takes the Code from his dad? I am getting an impression that the writers had plans on keeping Lelouch alive, initially. They came out and said the ending was left ambiguous for the reader to interpret as they want, and then, they removed that scene and declared Lelouch is dead.