Is this purported video showing the ending real or fake?
This is fake. Unless someone can point me to the dvd/blu-ray version this can be found on. Definitely not original airing.  Further more the art seems a little off to be Lelouch, (chin is a little sharp).  Chances are this is spliced in from another anime. 

P.S. - Not biased response, as I personally think he lived due to the Lelouch of the Rebellion movie they are working on as well as the popular code immortality factor.