Last month the Herald asked Lavery to confirm he had decided to investigate the matter, including details around its scope and time frame.
He declined to comment.
But email correspondence reveals that in response to Calvert's complaint, Lavery said he would follow up with each party involved as a first step.
He cautioned, however, that it was "very unlikely" he would be able to determine who Lester's email was actually intended for.
"As the matter has been reported widely in the media, regrettably I will have limited options available to me to obtain cooperation from the individuals involved as it has been made political", Lavery wrote.
Following that, in another email, Lavery confirmed he had received replies from all parties, but he was unsure how far a search of council's systems had progressed.
Calvert told the Herald the investigation was taking longer than she would have hoped.
The city councillor isn't so interested in who Lester intended the email for as much as how it got into his hands in the first place.
"I welcome the council continuing to give this matter due consideration", Calvert said.
When previously asked about the email Lester said it was a heads-up to Calvert that he had received an inquiry about ratepayer-funded mileage for councillors, which he was strongly opposed to.
"I have always treated all councillors with dignity and respect", he said.
At the time the complaint was laid Calvert said she wasn't sure whether it was a personal attack against her or politically motivated.
"Over the past month there has been a range of other petty information being leaked involving myself and others.
"I am deeply suspicious that they were also Justin, and that his email to me was actually intended for the media. If so, such information leaks may well be more than trying to harass me and at worst could be trying to undermine this Council as a whole, either by just himself and or with others."
In response to Calvert's allegations, Lester said he had little interest in having a public or private "spat" with Calvert.