You, along with every other person using the term Anonymous in this sense, seem to be immensely confused.
"Anonymous" isn't an organized group. It's a bunch of idiots who happen to browse a certain portion of the internet festering shitfest. That is it. Counted among their numbers, may in fact be world-class hackers, but that can be said of nearly any e-community.
Also, Lulsec is a group of scriptkiddies and hypocrites. "Freedom of the web, except for people we disagree with."