Ryan Ackroyd admitted one count of carrying out an unauthorized act to impair the operation of a computer.
Prosecutors say the 26-year-old accessed websites belonging to Sony, 20th Century Fox, the NHS, Nintendo, the Arizona State Police and News International between February and September 2011.
He will be sentenced May 14 at Southwark Crown Court in London. Other charges against him are being dropped.
Three other British hackers 18-year-old Mustafa Al-Bassam, 20-year-old Jake Davis and Ryan Cleary, 21 had previously pleaded guilty to launching distributed denial of service attacks on organizations including the CIA and Britain's Serious Organized Crime Agency. Denial of service attacks work by overwhelming sites with traffic.
Prosecutors say Cleary's targets also included U.S. Air Force computers at the Pentagon.
LulzSec, whose name draws on Internet-speak for "laugh out loud," shot to prominence in mid-2011 with an eye-catching attack on U.S. television network PBS, whose website it defaced with a bogus story claiming that the late rapper Tupac Shakur had been discovered alive in New Zealand.
An offshoot of the loose-knit movement known as Anonymous, LulzSec and its reputed leader, known as Sabu, had some of the highest profiles in the movement. But last year U.S. officials unmasked Sabu as FBI informant Hector Xavier Monsegur and officials on both sides of the Atlantic swooped in on his alleged collaborators, making roughly half a dozen arrests.