Ok so here is a VERY well done in depth analysis done by a comment on the English sub on anime haven (username: Lelouch Vi Britannia):

Did Lelouch really die or is he still alive? Actually, I can answer yes and no to that question. By reviewing several comments, which supports both perspectives, I have made some definite conclusions. These conclusions are supported by my own observations and are indicating that the one once known as Lelouch Vi Britannia is dead but yet alive. Currently, I have 11 points I use as evidence in this analysis:

1. First of all it is necessary to explain how the "code" is obtained by using Charles Vi Britannia, Lelouch's dad, and C.C. as an example. Charles' geass had already evolved into the advanced version, i.e. where it shows up on both his eyes, by the time the viewer get to know him. In addition, C.C. did also evolve her eyes before she received the code. In both cases Charles and C.C. killed their predecessors by using the power of their advanced versions of geass. C.C.'s predecessor also states this condition herself.
There is also another condition set before the code activates - one has to die. In the scene where C.C.'s predecessor tricks C.C., C.C. is wounded around her chest area with blood fussing out. Furthermore, Charles' code activates at the moment Lelouch orders him to die.
As in these two cases, Lelouch receives the code in a similar way, thus obtaining true immortality. When Charles grabbed onto his throat he was technically killed by Lelouch - he dissipated in this case - thereby passing on the code from parent to child. It also gives a lot sense that Lelouch receives the geass from Charles who is his father, and thus is the successor of both his ability, the code, and the throne.
However, it's important to point out that he didn't activate the code until the last episode where the last condition, involving the bearer's dead, was fulfilled at the moment Suzaku killed him. This realization alone is a very strong argument in that Lelouch is actually alive and immortal at that. There is further evidence supporting this point.
One should remark that C.C. also have the mark of the code on her forehead, while Charles has it on his hand. So Lelouch most likely has it on another part of his body.

2. Many critics points out that the creators of "Code Geass" declared that Lelouch Vi Britannia is no more. Now, it is true he actually did technically die, however, he is yet alive. Why is that? Well, the title of the second season is "R2". The reason is allegedly that the Japanese pronunciation of Lelouch would correspond to R in English of what I've read. In other words R2 is the same as R.R., similar to V.V. and C.C., and is derived from the name Lelouch, which goes with R as its initial.

3. Another evidence involves the name of the entire serialization "Code Geass". Why do you think it was called this? It is highly possible that the title is a combination of the abilities "code" and "geass". This hints that Lelouch in the end has both abilities. C.C. and Charles Vi Britannia didn't have both since they killed their predecessors and therefore losing their geasses. Lelouch didn't kill his predecessor C.C. but his father, thus obtaining the code while maintaining the geass afterwards.

4. If one pays close attention to the time after Charles dies, one can notice that Lelouch becomes more bold in his strategies, i.e. he shows up before his enemies more than before. That means he actually knows of his forthcoming immortality and he probably wouldn't have acted so bold if he didn't have this. He is a strategist that values his life when planning. An example of this is when he meets up with Nina face to face - she practically used to be a ticking bomb.

5. Another example of him knowing his own immortality is at the moment Suzaku stabs him. He shows confidence and doesn't seem like he is about to die at the least, it's actually like he's laughing inside himself for him being able to deceive everyone. Thus he is sure of his own position of being immortal.
Moreover, there isn't any kinds of flashbacks showing his time with Nunnally or his friends when he is stabbed by Suzaku, which is commonly seen when a main protagonist dies. Instead we hear words filled with confidence about destroying and creating worlds.

6. Another important point to make is that Lelouch has been close to the embodiment of cheats, lies, control, and manipulation - all in order to make a better world. This is also why he is one of the greatest characters of all animes. So why wouldn't he lie about his own death? Of course he would. That is why everybody, even the creators of "Code Geass", are acknowledging his dead. They want everybody to be fooled by Lelouch, of course, and it seems to be working just fine. Try to set yourself in the place of the creators. Would you really admit Lelouch was alive?
Lelouch is a pro and would never die, especially when Nunnally lives. He even fooled Suzaku by telling that he is influenced by the geass called "people's dreams" in order to make Suzaku also accept that Geass, therefore accepting his own inability to die at will. At the same time he assures a guardian for his sister Nunnally. He's truly an evil genius.

7. This and the following point involves C.C. Lelouch promised to make C.C. happy as she didn't manage to die. To maintain this promise he has to live. Before Lelouch dies she is begging, probably about him actually having the code. Afterwards in the carriage scene she is wearing a smile.

8. On the carriage C.C. states that the power of the king, i.e. geass, brings together people. This is told to Lelouch while she tilts he her own head upwards, indicating she is talking with the driver, allegedly Lelouch. Said statement bears the meaning that the world population have been brought together, however, it also includes individuals - of course also C.C. While she is smiling, she is together with Lelouch.

9. Now to further prove that the driver is Lelouch. The driver is wearing an identical collar to the collar Lelouch had before he was technically killed.

10. Another evidence that the driver is Lelouch is the paper crane atop the carrier, behind C.C. C.C. wouldn't bring such a thing and it most certainly is a symbol of Nunnally's and Lelouch's relationship. It is even a pink paper crane, a paper crane which was given by Nunnally to Lelouch in one of the early episodes.

11. The last evidence collected is that Mr. Orange is very loyal to Lelouch. He would never stand back and let Suzaku kill Lelouch that easily. Rather, he was merely standing and even smiled and pressed him onwards when Suzaku jumped on him. Thus he must have been knowledgeable to the faith of Lelouch.

Conclusion:
The creators of "Code Geass" left a whole bunch of evidence in order for people to actually reach the understanding that Lelouch is alive. This analysis is quite objective, i.e. it is built on elements in the anime. It is just like analyzing different literature, documentaries and other texts in society. It's all about putting oneself in the position of for instance the director, analyzing the personalities of the characters in the anime, and looking for evidence here and there. Thus you will reach this point.