Cleary has been charged with launching distributed denial-of-service attacks against organisations including the Serious Organised Crime Agency, the International Federation of the Phonographic Industry (IFPI) and the BPI. He is said to have breached his bail conditions over Christmas and is now being held in Chelmsford jail after being arrested on 5 March.
Cleary’s lawyer Karen Todner said that he had sent a handful of electronic messages to Monsegur.
Cleary, who suffers from Asperger’s Syndrome, is now due to reappear before a judge in May.
He was originally detained in a "pre-planned intelligence-led operation” in cooperation with the FBI, the Metropolitan Police said in June.
He was questioned at a central London police station on suspicion of Computer Misuse Act and Fraud Act offences. Computer forensics specialists were also examining a "significant amount of material" seized from his address.
LulzSec's victims have included Sony, the US Senate, the NHS and security companies linked to the FBI.
The group splintered from Anonymous, a digital activism collective best known for its cyber attacks last year against corporations such as PayPal that withdrew online services from WikiLeaks. Anonymous has been under investigation for several months by British and American authorities. More than 80 alleged members have been targeted worldwide.