Speaking in an interview with Gawker, the member calling himself Topiary said the attacks made by Cleary happened in 2010, which was before the group was even formed, sans the one he made on the British Serious Organised Crime Agency (SOCA) on June 20.
LulzSec contends Cleary hacked the site after the firm had already tried to bring it back up from an attack it had performed earlier that day.
"Ryan isn't part of LulzSec… No LulzSec arrests have been made," said Topiary. "Our Twitter hasn't even been suspended. The mass media are clueless and have spun 'LulzSec leader' out of their own asses, when there are no facts to support that Ryan is related to LulzSec," he said.
Topiary goes on to say LulSec's only connection with Cleary was that he ran a chat server with a "fan room" for supporters of the hack group.
"We had identical fan chats on 2600, AnonOps, Efnet, Rizon, Unreal, etc…" said Topiary.
The Lulz member went on to say it's next venture, which is called Antisec, targets government agencies and banks with goal being to steal secret documents and leak them onto the net.
The first document released pertained to the Arizona Department of Public Safety, and situational awareness bulletins from the Arizona Counter Terrorism Information Center, which according to excerpts on BoingBoing, reveals more than "700 bulletins, email archives, images and other files," in a 440MB pack releases on a torrent site.
The documents detail subjects "ranging from internal training, policies, events and goings-on in the criminal underground."
"Every week we plan on releasing more classified documents and embarrassing personal details of military and law enforcement in an effort not just to reveal their racist and corrupt nature but to purposefully sabotage their efforts to terrorize communities fighting an unjust 'war on drugs'," said a statement from LulzSec.
You can read up on more of this through the links.