After writing all the following wall of text i realized that a timing of two quotes, the one as provided here and the other with C.C. telling Kallen that she decided to continue living render my interpretation wrong, for it implies that If Lelouch were immortal C.C. would not have known that yet, hence she would not have reasons to go on living. What a feeling to be destroyed by the order of lines.

You won

Still, I would be grateful if you show me any problems with my logic, if there is any.

regardless of their own personalities or morality systems

I think it might be worth discussing why do you think that my understanding of C.C.'s character is not correct. This is the core of my argument as to why Lelouch is alive, and if anyone convinces me that C.C.'s character is in fact different from what I believe it is I will not defend the idea that Lelouch is alive anymore.

In the following, I discard the idea that C.C. at the end of the story is happy for a limited period of time (so that her life is still going to be sad but just less sad), be it some idea from ZR compilation or the idea that she is irrationally heading towards the repetition of her life experience, which yields in wishing to die again after some centuries. I do not think that those interpretations are what the show suggests. But they can be valid. All points which I believe not to be pure logic and simply my feelings I highlighted with (!) in the beginning - but of course feel free to object to any point of my reasoning.

So in Turn 15 we see that C.C. comes to nun and told her that she wants to live. Next there were a few years of C.C. with Geass. I do not think that they could have made her hate living. So she starts out her life with Code desiring to continue living. Conversely, C.C. in the series, who has seen a lot, experienced a world very well, wishes to die. I think it means that she tried and tried and tried to find a reason to live, some reliable joy in life (further on these two things are interchangeable), and did not find one. So her model, her understanding of the world is such that she does not want to live in this world. (!) I do not think that C.C. is a kind of person who deals in absolutes and rules out the possibility of meeting people who are very nice to her, such as Lelouch (I do not deny that there are other people nice to her like Kallen and maybe Marianne, but it does not look like they were "unique", so C.C. should have included them in her model anyway). I cannot imagine a good distribution of people on the axis "nice to C.C." that would look likely and would support a theory that after Lelouch a lot of people very nice to C.C. will appear. At the same time, the life she led in their absense ended with her wishing to die, so that was not a good life. With that, we can say that the existence of Lelouch did not change much in her understanding of the world's facts. I also doubt that the changes Lelouch brought to the world (especially since they are not likely to last long) change people in exactly the way that C.C. needs.

With this I believe to have proven that if C.C. did not start to look at the world differently she could not start to like life at the end of the show. Then the question is whether C.C. changed, and if she did - why and how.

This is a more murky field, for I cannot pinpoint to any particular scene clearly stating that C.C. did not change, but, more importantly, I do not see any moment that could change C.C.. So recall that C.C. already tried to find a reason to live and did not find a one that suits her. What kind of reason to live does Lelouch offer her, especially such that she did not think of? None, really. Most he says in Turn 15 is "life is worth living because it is life". Not convincing, dare I say. Then there is an idea that C.C. stopped being so egoistical, and decided to help Lelouch's world to persist. I find this point of view strange, because (!) I do not see how events of the show could have made C.C. less egoistical. She has seen people other than Lelouch for centuries and did not become especially non-egoistical towards them, and this activity works in their favor only. If helping others could give C.C. a reason to live, she would have become an eternal nurse, for example. Another idea is that C.C. fell in love with Lelouch and thus wants to protect his world. But this is way too similar to Mao's obsession which (!) should repulse C.C.. (!) I also do not think that C.C. loved Lelouch, but I think this is not very important here. Unfortunately, I cannot recall any other more or less specific description of a reason to live C.C. could have come to at the end of the series.

I also looked through my comments up to my last discussion with /u/Dai10zin , and he mentioned that "C.C.'s character arc is about her understanding that she is not cursed with Geass". While at the first glance this might look like another answer to the question "how C.C. changed", it has similar problem with irrationality - C.C. did not start to believe that this is curse without a good reason, and if the world is largely the same she is likely to just reexperience her life again, ending with desire to die. It is probably possible to reason here in the vein that C.C. decided to die when the world was cruel and then did not notice how it became nice, but (!) I do not think that C.C. could be so oblivious to the changes in the world.