[MENTION=5684]Elfboy[/MENTION], I know you were doing it in a loosely correlated manner but my 4 wing didn't like that. Anyway, as for Lelouch being a 6w5, I can't see it. Where's the holy faith in him? Where's the doubt, the questioning, the inability to believe in hmself and what he knows and that of authority? [MENTION=17134]PimpinMcBoltage[/MENTION], same about beta-ness. So I'll just shoot both of you down here because I don't think he's a beta NF 6w5 and here's why:
In episode 6 of season 1, I think the differences between beta NF and gamma NT is perfectly illustrated. What you need to realize are the differences exhibited in behavior between Lelouch and Milly, the latter a clear beta NF type, I'd wager EIE. In fact, most of the students at the academy seem to be Fe-oriented with the exception of Lelouch, Suzaku (EII-Ne 1w2 so/sp or possibly so/sx) and Kallen (most likely ESI-Fi 6wx sp/sx). What you see going on at the academy are mostly beta antics. Lelouch's ability to plan and think ahead are not 6w5 traits but clear Ni and Te traits. There's nothing inherent about the 6w5 sp type to be able to plan ahead. If anything, what you'd get is most likely an intensely private and most likely rather phobic 6. Even if we assume that Lelouch is a 6 and is counterphobic he is clearly not 6-reactive. This video is one of the best there is in showcasing 6 and 4 reactivity:
DiCaprio's character is a clear 6. Notice the superego drive of never being wrong. Lelouch doesn't have that and while I'm about 1/3 of the first season, I have yet to see Lelouch act or behave in this manner. He's clearly a narcissist. Look at how he loves the attention directed towards Zero, and when he acquires the Geass he's not concerned about the moral consequences of what it means using it as a 6 most likely would, instead, he simply sees it as a way to further his goals. He clearly does not care much about other people's feelings which speaks inherently against beta NF, even beta NF gone wrong. No, his masterplan is of impersonal structure - he is going to take down the Britannian empire despite that pretty much everyone has told him that it's not possible. How's that not narcissist? Heck, compare him to Sephiroth after he went insane and you realize the differences because Sephiroth's logic is still weirdly Fe-tinted. He's going to unite with his mother and further his mother's plans to destroy the planet and then the rest of the universe. Where's Sephiroth's focus on his personal desires? No, what he does is that he takes on the desires of JENOVA and he literarily becomes JENOVA. That's twisted Fe logic for you.
You also forgot that 7 has a connection to 5 so a 7 will naturally take on some of the traits of a 5, especially since 5 is the soul child of the 7. What you see from Lelouch is mostly a positive outlook attitude of things working out because Lelouch ultimately trusts himself and his abilities almost to a fault which can come across as a carefree manner. That's narcissism and id drive and the greed kicks in because it's not just enough to free Japan, no, he's going to take down the entire Britannian empire by himself but whereas other types who might claim the same thing, for instance 6s, might ultimately bark louder than they bite but ultimately waver, Lelouch can actually do it. He's very aware of his abilities and the limitations of them, and I'd say that's a strong argument that showcases his connection to 5.
Furthermore, not once are we shown that what he seeks in life is ultimately some kind of stability nor do we see him seeking out authority figures. His rejection of his father and the Britannian empire rather seems to be based on 8 anger and drive, especially because of what they did towards his sister. It's revenge that he seeks, not because he wants to show the world the truth or because he ultimately distrusts society itself. One could perhaps even make a compelling argument for sx/sp 8 but I feel that Lelouch has ultimately a positive outlook on life and while a dog-eat-dog mentality drives him forward, it doesn't seem to be the core outlook that defines him.
Also, another way to clearly discern the differences between Lelouch from being a 6 is simply comparing him to Kallen who is a 6 which became very evident in the bathroom scene in episode 3. Furthermore, Lelouch's Te couldn't be more evident in how he figures out the limits of the Geass powers. It's all Te data: You can only use it once per person, there seems to be no inherent limit to how long the power lasts, you need to be in direct eye contact for it to work etc. Te creative makes very sense for him.
The there's Fi that shows itself in that Lelouch's morals and ethics are not driven based on external expectations but based on his personal ethics. It's always about how things make him feel, not how others feel. He's not going to destroy the Britannian empire because it's good for the people or Japan or any other Fe reason someone could come up with, no, he's going to do it because he thinks his father is a douchebag and allowed his mother to be killed and his sister to be put in a wheelchair. It's very personal.