Was Lelouch the person driving the cart in the last scene of Code Geass R2? At the ending of Code Geass R2, the last scene showed someone whose face wasn't showed riding a horse-pulling-cart with CC. I believe that it is indeed Lelouch (who was previously stabbed by Suzaku wearing Zero's uniform as part of their Code Zero plan to free Elevens), and that he had gained immortality because of his frequent usage of his Geass. 

Lelouch's Geass first leveled-up the episode when he accidentally ordered his sister Euphemia to kill all Elevens. Then, his father King Charles was beaten by him and I'm thinking that King Charles' immortality was transferred to him. 

If that person was really Lelouch, then, has he already gained immortality by that time?
This seems to be a religious issue, judging by the amount of arguing I found while I was searching for the information contained in this answer. At the very least, xjshiya's answer is not universally accepted, and there are a lot of people who flat out reject that theory. In my opinion the evidence against the other theory is more compelling. I'm going to try to present said evidence as impartially as I can.

First, no official source has ever claimed that Lelouch survives at the end of R2. That alone doesn't answer the question, because it could be deliberately ambiguous. Of course, Lelouch would need to be alive to be driving the cart.
Second, several official sources list Lelouch as dead at the end of R2. Here is an interview with writer Ichiro Okouchi, taken from the Japanese magazine Continue (vol 42, Oct 2008, translated into English (I have not yet found the original so I can not confirm the accuracy of the translation). I've copied the relevant part below:

&quot; -----Still, isn't it possible that defeating the wise ruler Schneizel, the person who was supposed to have brought order to the world, might lead to some [viewers] interpreting it as a Bad End?
Okouchi: That's true. There are probably a lot of people who think of it as a Bad End, a tragedy, considering the protagonist's, Lelouch's end as well. However, Lelouch says in the first episode: &quot;Only those prepared to be shot are allowed to pull the trigger themselves.&quot; If you were to think of that as his pride, then I think his getting shot (killed) in the end was a logical end. Of course, I understand that not all of the viewers will accept this ending. There were people who wanted a happier ending, after all.
-----Was there a dispute among the staff members regarding the ending?
Okouchi: No. It was decided fairly naturally. During the &quot;Code Geass&quot; script meetings, there are many cases in which there were a number of disputes, but there were barely any when it came to the scripts for (the previous series's) episode 25 and the final episode. I think everyone felt the same when it came to the end of the character that is Lelouch.
-----Why were you so bold as to choose this ending when the viewers might see it as a Bad End?
Okouchi: Bold... yes, we were so bold as to chose this ending. Perhaps the show that is &quot;Code Geass&quot; ending up this way was decided the moment Director Taniguchi and I teamed up. I suppose you can call it our sense of aesthetics, or perhaps a part of our psychological makeup.
...
------I see. So Lelouch's decision was also your, Mr. Okouchi's, and Director Taniguchi's decision.
Okouchi: Which is why I think of both our and Lelouch's decision as Happy Ends. I believe that there will be better things in the tomorrow awaiting Nunnally, Kallen and the rest who have been left behind. And surely Lelouch, who was able to make this into a reality, can only be happy [about this].
...
-----Some unresolved mysteries still remain.
Okouchi: From the very beginning, [I/we] never planned on explaining everything. In fact, if you ask me, I think we might have overdone the explanations. While it's undeniable that Lelouch's story has ended with a full stop, the other characters' stories are still on-going, and it's not like the world [of Code Geass] itself has come to an end either. [I/we] didn't want to end it by closing it up for good.&quot;

That seems to pretty strongly confirm that at least Okouchi believes Lelouch dies in the end. Of course, Okouchi, being a writer, doesn't have the final say. The director is the one whose word we should ultimately be looking for, but director Gorō Taniguchi has not said anything definitive either way. He did say something ambiguous, to the effect that he &quot;prefers to see the end as a happy one,&quot; but Okouchi also claims it's a happy ending despite Lelouch dying. Okouchi also didn't seem to have any difficulty speaking for the whole team, and no one came out to correct him, so this seems reasonable.
The link above has a couple other relevant quotes which I will not repeat here. I believe that this establishes that there's a pretty strong opinion that Lelouch is, in some form or another, dead.
Here's a further confirmation of this. This image lists people who died in R2. I've boxed the relevant entry for Lelouch.

The above was taken from the same issue of the magazine. This is an official image. I don't think this really adds anything to the above except removing some ambiguity.
There's some further evidence here (I haven't really checked this translation but by a cursory skim it seems to be accurate).

C.C.’s profile has also been updated, and the final part of it now says: “Knowing that Lelouch does not hate her for giving him the Geass, she is now able to show her true feelings. With the realization of “Zero Requiem”, her time with Lelouch, who was able to forgive and accept her, came to an end, but the memories created with him has, without doubt, saved her from eternal loneliness.”

Given that the &quot;Lelouch = Cart Driver&quot; theory requires that Lelouch and C.C. aren't separated at the end, this piece of information just doesn't make sense unless we reject that theory.
So we've confirmed that Lelouch is pretty dead at the end of R2, and that the fan theory that he is the cart driver really isn't supported by the official statements. There are a couple of ways to get around all of these facts. I don't really regard them as anything but conspiracy theories and other ways fans are trying to deal with the ending that isn't quite as happy as they were hoping for.

Lelouch has at least two identities. Perhaps Lelouch vi Britannia died, but Lelouch Lamperouge lived on? Or maybe Lelouch abandoned his name, but he's still alive, and the sources list him as dead because his identity as Lelouch vi Britannia is dead? I can't really argue against the possibility of this, but there is no evidence supporting it at all. It doesn't really make sense in light of the C.C. bio either.
While several people have confirmed that they believe Lelouch dies, director Taniguchi has been notably silent. Perhaps there was some disagreement among those in charge, and Taniguchi actually thinks Lelouch is alive? We can't ever know for certain what happened when they were writing the ending, but it seems reasonable to expect that if there were disagreements, Okouchi wouldn't have claimed that there were none, and if the disagreements were major someone else probably would have spoken up.

Again, I regard those as little more than conspiracy theories by disgruntled fans who think the ending is somehow &quot;unfair&quot;. There is no evidence supporting either of them.
While the theories proposed in the other answer are good speculation, they just don't fit with facts released later. The consensus of the production team is that Lelouch is dead and not driving a cart at the end of Code Geass R2. The cart driver is probably just some random guy. If this seems unfair to you, then it's worth remembering that many other characters with far fewer crimes died in the series, so in some sense it's poetic justice for Lelouch to also die. And the interviews with everyone including the director do confirm that in dying, he was successful at his goal of starting the world down a better path.
Again, this seems to be something people view religiously. I'm not claiming that the speculations that Lelouch survives are bad in-universe, but there's simply no evidence for them either from the producers and a lot of evidence to the contrary, so the better answer in this case is that Lelouch is dead.