I have a firm belief that he is still alive. Here are a few reasons:

- After he fought and vanquished Charles Di Britannia (his Dad) and destroyed the thought elevator in the world of C, both of his eyes contained the power of Geass. When he killed Charles, he STOLE his immortality.

- CC adresses his in the last line of the final episode. "Isn't that right, Lelouch?" Many people would assume that she was speaking to his spirit of something of that sort, but I have reason to believe she was speaking to him directly.

- The final and most pressing reason is probably this. If you have seen the final episode, near the end there is a man driving the hay cart which CC is lying on top of. I paused the movie and took a screenshot of the moment where you can best see the cart-driver's face, then zoomed in. If you look closely at the image you will see his hair and signature purple eyes. I strongly believe that this is Lelouch.

Thank you for taking the time to read this. :D