Correspondence leaked to the Daily Post revealed Merseytravel chief executive Neil Scales had written to Prof Brown warning of potential legal action over Prof Lesley's criticism of the tram project.
In a reply to Merseytravel in January 2002, Prof Brown said he hoped Prof Lesley's comments would not disturb the positive relationship between the university and the company.
He added that Prof Lesley may wish to "consider his position" after being reminded not to express his views on behalf of the university.
He wrote: "If you decide to take action against Prof Lesley, you should do so on the basis that he is a private individual."
Prof Brown said Prof Lesley would not receive any support from his employees.
Prof Lesley was sacked for gross misconduct in March 2003. That year, he received a five figure sum, believed to be close to £100,000, in a settlement claim for unfair dismissal.
The union claimed JMU failed to protect the transport expert's academic freedom to speak about public projects.
It says Prof Brown should have revealed the letters presiding over the disciplinary hearing that led to Prof Lewis' sacking.
A spokesman for JMU said: "It is with great frustration that Liverpool John Moores University again responds to yet another missive from Natfhe pertaining to the long closed case of Professor Lewis Lesley.
"Reluctantly, the University now feels compelled to state that it strongly objects to the mis-information being continuously disseminated by the Union to its members at LJMU and through the media.
"It is unfortunate that many years after its conclusion, Natfhe seem unable to let this case rest in peace.
"LJMU has complained formally to Natfhe's central office about the activities of the full time Regional Official and awaits their response with interest."
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