This is why I think she's an ENTP. She's often compared with Madonna, an ESTP, and they have a lot in common. But Lady Gaga is involved in creativity and originality just for the sake or originality and creativity, wich is more an NP trait. ENTPs often make ESTPs look "normal" and down-to-heart. On other hand, she make every superstar and pop icon like Prince or Michael Jackson, or even Mick Jagger, look like pure wanabee. The theory is that she envision and understand globally what a superstar and pop culture is and achieve that idea in a concrete way. So, Ni-dom and inferior inspiring Se. At the same time, she has that meekness wich sounds more Fe, so, INFJ. Prince was an INFJ after all. She's the Andy Wharol of the 21st century in some sort, and Andy Wharol was an ISFJ. On the LGBT video, she takes very authoritarian positions, wich sound more ENTJ, but I don't think she is.
Especially in comparaison wih a true ENTJ like Ellen Degeneres:[youtube=TFgTP47R4Ic]Lady Gaga Interview on The Ellen DeGeneres Show[/youtube]
As for her enneagram, she's been typed as 6w7 Sx/So, and I think it's right. That could explain why she has been mistyped as 3w4, 4w3, 7w6 and also 7w8.