An email Woolf sent to Lavery and two council officers at the time shows the councillor had asked to meet Zoo Trust Board chairman Craig Ellison.
"The meeting request is to seek clarification as to processes around the Zoo Trust Board", he wrote.
In reply to Woolf's email Lavery said the Board had looked into matters and since the conclusion of those considerations, it was satisfied with the processes undertaken.
He also referenced public statements by the council's then Board representative Councillor Peter Gilberd who said he had full confidence in Zoo management.
Lavery wrote he was surprised Woolf was again seeking a meeting with the chairman.
"When the Mayor and I met with you on Tuesday, you agreed that it would be inappropriate to engage in an employment matter between the Board and the staff of Wellington Zoo given it is an over-reach of your role and authority following comments you had made to media."
"I would urge you to honour your agreement of yesterday to step back from any involvement given it is an employment matter."
The comments Woolf made to media about bullying claims at the Zoo were in his capacity as chair of the Council Controlled Organisations Subcommittee.
The Dominion Post article from April 9 said Woolf "would investigate the allegations, though his mandate could only look at whether the board had behaved properly".
The exchange over the Zoo unfolded just a few months before Woolf again made comments in the media, this time about an Employment Relations Authority decision, which looked into alleged bullying of a former council staff member.
Behind the scenes Woolf accused Lavery of "spin" and a "lack of good judgment", while Lavery accused Woolf of creating inferences in the media that "could not be further from the truth".
Lavery went on to tell Woolf "I feel that I have no option but to raise this directly with the mayor".
On Tuesday, Mayor Andy Foster confirmed a meeting was being held over the code of conduct investigation matter this week.
"I want to understand what has actually happened and who has said what to who and whether we actually need to do anything further about it", he said.
When the Herald asked the mayor's office whether the meeting had gone ahead and what the outcome was, a spokesman declined to comment.
Lavery and Woolf declined to comment.