Hacking is not that difficult nowadays. NSA, CIA, FBI, etc have been hacking all other government and cooperate systems. They even have backdoors to many widely used encryption standards such as DES - which make them access "secure" systems even without having to break them. They access a lot of shit all over the world just silently and successfully. Russian and Chinese hackers are not that powerful as the US agencies.
LulzSec wanted publicity, that's the only difference between them and most of the other hacker groups. They were not the best hackers, may be one of the best though. By advertising their attacks 1. They exposed the insecure nature of the systems to everyone 2. They motivated the people of similar interest to involve in similar activities - which pissed off the federal agencies and got them hunted down.
Their advertisement was the biggest headache to the federal agencies, than the attacks.