A statement published on a file-sharing website said that its “planned 50-day cruise has expired”.
The group leapt to prominence by carrying out attacks on companies such as Sony and Nintendo.
Broadcasters Fox and PBS, the CIA, and the United States Senate have also been cyber-attacked by the group.
As a parting shot, the group released a selection of documents apparently including confidential material taken from the Arizona police department and US telecoms giant AT&T.
Correspondents say LulzSec’s announcement could be a sign that its members are nervous because of recent police investigations, including the arrest of a British man suspected of links to the group, and efforts by rival hackers to expose them.
The group’s identities remain anonymous and it has not been possible to contact its members directly to confirm its statement.
The statement said that “our crew of six wishes you a happy 2011”.
“So with those last thoughts, it’s time to say bon voyage,” it added.
“Our planned 50 day cruise has expired, and we must now sail into the distance, leaving behind – we hope – inspiration, fear, denial, happiness, approval, disapproval, mockery, embarrassment, thoughtfulness, jealousy, hate, even love. If anything, we hope we had a microscopic impact on someone, somewhere.”
But LulzSec urged its supporters to carry on.
“We hope, wish, even beg, that the movement manifests itself into a revolution that can continue on without us,” the statement said.
“Please don’t stop. Together, united, we can stomp down our common oppressors and imbue ourselves with the power and freedom we deserve.”
The group had previously told the BBC’s Newsnight programme that it wanted to target the “higher ups” who write the rules and “bring them down a few notches”.
In an online Q&A, the hacker known as Whirlpool, who described himself as “captain of the Lulz Boat”, said that while the group had begun hacking “for laughs” – for which the word “lulz” is cyber-slang – it evolved into “politically motivated ethical hacking”.
And in an interview with the Associated Press on Friday, a LulzSec member said the group had at least five gigabytes of “government and law enforcement data” from around the world, which it planned to release in the next three weeks.
Ryan Cleary, 19, from Wickford, Essex, was arrested as part of a Scotland Yard and FBI probe into LulzSec and charged with hacking the website of the UK Serious Organised Crime Agency.