Lelouch is definitely alive!

Final Scene
“Geass is the power of kings, and it will isolate you…Looks like this isn’t the case, right, Lelouch?” said C.C. as she tilt her heads upwards and raised her voice. This implies the cart driver (who conveniently has his face masked and hidden) is Lelouch and C.C. is speaking to him. The final line also means that Lelouch is not alone because he now has C.C. Additionally, he has a promise to keep, that is to make C.C. happy.

Pink paper crane – No reason for C.C. to keep it (and the possibility that she doesn’t know how to make it). It could be a memento of Nunnaly kept by Lelouch, not to mention that Nunnaly is the one who taught Lelouch how to make it.

“The biggest, most undeniable giveaway is the camera work. It is done in a way to purposely draw attention towards the driver, but simultaneously not enough to show who he is and keep his identity hidden. Combined with the slight head tilt and delivered line from CC, it's a done deal.” (FreezeGeass, Animesuki forums)

Lelouch has the Code (Either from Charles or C.C.)
Only Code immortals can transfer memories, as such is the case when Nunnaly touched Lelouch and realize what all his plans are about (accompanied by the trademark Geass “zzzng” sound effect).

Consequently, only fully developed Geass users can obtain the Code, which Lelouch is as he has double Geass eyes. This foreshadows that Lelouch is able to receive the Code. He could’ve obtained the code from Charles when he was grabbed by the neck (he doesn’t appear to be in pain when choked).

It is also possible that he obtained the Code from C.C during the 2 month period before his ‘death’.

Jeremiah’s Reaction
As one of Lelouch’s most devoted and loyal subordinates, he seems awfully cheerful and even smirked when he let Zero / Suzaku went pass him to kill Lelouch. It could be that he knows Lelouch’s immortality beforehand.

Show’s Title: Code Geass R2
R2 could imply Lelouch’s new immortal name (like C2). In Japanese, Lelouch Lamperouge is pronounced Rurūshu Ranperūji hence R2.

Code Geass also indicates that Lelouch has now gained both, the immortality Code from Charles and the power of Geass from C.C.