They came to be when they got fed up with how Anonymous was working so they broke off from that "organization" and made their own "hacking" group. But once their dox got exposed, they came crawling back to anonymous and attempted to re-join them. They also started #Antisec which is an operation to hack government websites since they got mad at their leaked dox and are afraid of getting vanned.
Heavily doxed by the Web Ninjas and have drawn the ire of th3j35t3r, who has also made attempts to identify them. Ryan is now arrested. LulzSec claims that Ryan wasn't really a member and that he just hosted their IRC channel. They've also angered the more volatile hacking group, TeaMp0iSoN. GG. GG.
Lulzsec came out of early retirement and intervened in the UK phone hacking scandal. They planted a fake story on The Times website saying that media mogul Rupert Murdoch had committed suicide at his home. When the site was taken down Lulzec then redirected The Times homepage to The Lulz Boat's twitter page. On the next day some 20 Anonymous members - who were mostly from the US - got V&; and one alleged Lulzec core member, tflow, was reported to have been arrested in the UK. All were connected to DDoS attacks on Paypal, Mastercard and others in concert with Operation Payback.