Lulzsec is funny and clever, but they haven't attacked a really big name site. But if they were real hackers, they would have tried to take down Facebook, E-trade, WoW, etc, something to generate an enormous amount of press. Instead, they've attacked small sites, security companies that didn't exist until a few months previous, and they attacked the CIA website. They've generated a lot of light, but not a lot of heat. For someone with their level of coordination, they certainly are trying to get themselves caught by posting on Twitter, going on IRC, leaving voice traces, etc. I don't buy the idea that they are complete nihilists, it's too exhausting.
The only thing I can think of is that these guys really are CIA, and they're trying to get blackhat credibility, in order to infilitrate and take down Anonymous. Sure, there's some collateral damage, but it's for the "greater good", right? My only hope is that I'm wrong, but I doubt it. The fact that they've teamed up with Anonymous after only a couple of months in existence makes me think I'm right.