I've heard of anon but never lulzsec!
It doesn't matter. It was just a grouping of more talented Anonymous hackers who started working together.
The .gov just doesn't get the concept, or does not want to acknowledge it. Anonymous... is anyone following the loose and ever shifting ideals, or likes/dislikes of Anonymous, and who says or does not say they're acting as Anonymous. That's it.
There's no hierarchy, there's no leadership. It's not even a traditional resistance cell structure.
It's a mob. Some are skilled, some are just script kiddies, some are just moral support, or in it for the lulz.
The .gov or other powers that be can snipe a group of the more talented hackers that rises up and starts doing enough things to make themselves traceable, but there will be another such group tomorrow, or in a week, or in a month. Either have your INFOSEC be truly airtight, in both technical and human terms, or don't piss them off. Ideally, do both.