The third point alleged he had "no issue with paedophiles being able to express themselves, or subjecting children to individuals with sexual proclivities targeting children".
It also alleged Lockhart believed in bullying people who did not conform to his views.
It said if his workplace continued to employ him "we will consider that an endorsement of the above qualities'' and notify others, including clients and media.
"We do not take issue with your business, only one person within it that was likely employed without knowledge of this person."
Whoever wrote the email claimed they were "more than happy to provide overwhelming evidence for any of the points above".
Lockhart's employer did not want to be named and declined to comment in order to protect other staff.
Lockhart told the Bay of Plenty Times the email was "just hideous" and included "nonsense and defamatory" accusations in an effort to threaten his employment.
"I felt it was absolutely appalling I was being put in the position of having to deny allegations, that are of course completely untrue, but simply because of my being a civil rights activist."
He believed the allegations were retribution for having stood up against what he felt was intolerance and injustice.
He said it was "widely circulated" among the staff at his workplace and submitted through a website online inquiry form.
"It's just absolutely disgusting someone would behave in that way. But it's not surprising if I am honest,'' he said.
"The idea that someone is trying to threaten my job ... that's what makes it so poisonous."
He said it was particularly concerning how whoever wrote the email drew parallels between the accusations and being gay.
"There is the hideousness of people thinking that's what being gay is. It's horrifying," he said.
"The association that standing in front of the school talking about discrimination, somebody can then level that sort of argument. It's just appalling. There are no more words for it than that."
The email had been reported to Netsafe, he said. Netsafe was approached for comment.
Neighbourhood Support New Zealand (NZNS) chief executive Tess Casey confirmed the email address was not associated with Neighbourhood Support New Zealand or the local member organisation in Tauranga.
Casey said it was important to reinforce that Neighbourhood Support and Neighbourhood Watch were not "one and the same". There had not been an official Neighbourhood Watch organisation in New Zealand since 1999.
"We are not aware of any official network called 'Tauranga-wide Neighbourhood Watch' and the fact that no one has put their name to the letter is probably an indication that this letter is not sanctioned by an organisation."
