I'm going to go ahead and say that what Lulzsec is doing, will ultimately only favor the world as we see it.
Why? Let's start from the top.
I'm fairly sure that a lot of young internet active people are intrigued by the concepts of hacking already. And as always happens when someone or something appears as a paragon for a specific area, the current activity of Lulzsec will surely cause a lot of people to look into hacking, as it seems to be a pretty fun and exciting thing to do.
A lot of these young wannabe-hackers will never get to where they want, and either give up or do something so stupid that they get caught red handed. But some, a small click, might actually learn enough to become competent hackers.
This will, in turn, mean that the internet security highway opens up, as new targets - untagged targets - are always goals to be reached for any hacker on the rise.
Why is this a good thing? Any hacking made agains't a website, causes that website to seriously overlook their own security. Because spending a sizeable part of the budget on extra internet security is far cheaper than a huge-ass lawsuit-
Is Lulzsec doing good things? Not directly, no. But imagine the results of what happens. Yeah, the DDoS attacks are harmless, but they HAVE actually hacked and obtained information from quite a lot of websites (Bethesha Game Studious, British NHS, Nintendo, Mediafire, InfraGard etc) - don't you think that most of those websites and their affiliations will overlook their security and, ultimately, make them much more secure for it's users?