In a legally recorded telephone conversation heard by Fairfax Media and provided to NSW detectives investigating the Sydney Yeshiva cases, Rabbi Lesches admitted to counselling the alleged abuser upon learning he had sexually abused a boy a decade his junior.
Rabbi Lesches is now one of New York's leading ultra-Orthodox figures.
Rabbi Lesches said he told the man that both he and the boy would be forced to leave the Yeshiva community if he could not control his urges.
"If not, both of them would have to leave," he said.
Rabbi Lesches, who never informed police of the abuse, said he did not know the man had ignored his warning and gone on to sexually abuse at least three other boys in the late 1980s.
He said other Yeshiva leaders were responsible for supervising the man.
In the conversation, Rabbi Lesches suggested one of the man's victims, who was aged about 11 at the time of the abuse, may have been a consensual partner. ''Everyone was telling different stories and trying to put the blame on someone else,'' he said.
"We are speaking about very young boys â€¦ everybody says about the other one that 'he agreed to this'."
When challenged on his position that young boys could give consent, Rabbi Lesches replied "you would be surprised'' and added that some non-Jewish boys, who he termed "goyims", began acting or thinking sexually ''from the age of five''.
He said teenagers from poor backgrounds had ''nothing else to do in life, only thinking 24 hours about sex'' with each other, members of their own families and even ''dogs''.
Rabbi Lesches also said reporting the alleged abusers to police so many years after incidents occurred would ''destroy them and their children'' and cause pain for victims.
''Do not talk this way... when it is such a long time ago, everybody suffers,'' he said. ''If you start to do something about it will not be productive and not be good for nobody.''
A traditional rule, mesirah, prohibits a Jew from reporting another's wrong-doing to non-Jewish authorities; it remains a powerful influence in some ultra-orthodox communities.
Rabbi Lesches, who did not respond to questions from Fairfax Media, is the third senior rabbinical leader to be identified as having known something about the abuse of boys at the Sydney Yeshiva in the 1980s.
In February, Fairfax Media reported how the alleged perpetrator, who was sent overseas, had recently admitted guilt to some of his victims. He told of how the centre's spiritual leader, Rabbi Pinchus Feldman, once warned him to stop what he was doing.
In response to that story, Rabbi Feldman released a statement saying he had no recollection of anyone confessing to him their involvement in child sexual abuse 25 years ago.
In early March, another senior rabbinical leader, Rabbi Moshe Gutnick, admitted he did not contact police after a young boy contacted him more than 20 years ago to report sexual abuse at Bondi's Yeshiva.
Rabbi Gutnick, who heads the Organisation of Rabbis of Australasia, said he received an anonymous phone call and alerted senior members of the Yeshiva to the boy's claims. He said that with the benefit of hindsight ''I would have probably called the police''.
Rabbi Gutnick is understood to have told Bondi detectives recently all that he could recall about the phone call. In a statement published in the Australian Jewish News this year, he said he ''felt deeply saddened that I had not recognised what I only now know was a legitimate cry for help''.
''I appeal to the entire community -- to victims and their parents, to community members and leaders. If you have information please come forward to the police. Don't be afraid,'' Rabbi Gutnick urged.
The Sydney Yeshiva Centre said it has comprehensive child protection policies in place and the centre had liaised with police over the allegations. In a statement the centre said it ''unequivocally condemns any form of abuse'' and treats its child welfare responsibilities with the utmost care.
''Yeshiva... has always endeavoured to comply in full with all its legal and moral child safety obligations.''
Fairfax Media can also reveal that the family of the man being investigated by NSW Police over the sexual incidents at the Bondi Yeshiva are big financial supporters of the New York Monsey ultra-orthodox community led by Rabbi Lesches.
The alleged abuser was also appointed to the board of an Australian company involved in providing educational materials for Jewish students, years after his abuse of boys.
The alleged abuser has in recent years been sheltered by a leading Los Angeles Jewish welfare group, with 2011 emails between the man and one of the organisation's senior members showing he was in danger of having his past in Sydney exposed.
''I have no idea how anyone found out - but calls are coming daily from many sources. So far, we've been protecting you,'' wrote an executive director at the LA organisation in an email to the man.