Then-acting merit protection commissioner and ex-NSW ombudsman Bruce Barbour told a complainant this month an inquiry into the allegation would be conducted.

In an email sent in June and seen by Fairfax Media, the complainant alleged Mr Lloyd breached a code of conduct by using his Australian Public Service Commission email address in October when writing to the head of a right-wing think tank following questioning by senators about his links to the group.

The complainant on June 3 asked the former acting merit protection commissioner Mark Davidson to investigate the email and alleged it breached the public service's code of conduct.

Mr Davidson, whose substantive role was in the public service commission, wrote two days later telling the complainant of his conflict of interest, saying he may need to refer the allegation to an independent person to consider.

In an email sent on July 9 Mr Barbour, filling in for the incoming permanent merit protection commissioner Linda Waugh as she took pre-arranged leave, told the complainant he had decided on an investigation but did not say when it would start or finish.

"You will be advised when actions arising from your complaint have been finalised," he wrote.

Ms Waugh, who took over from Mr Barbour on Monday, declined to comment "on any complaint, review or inquiry matters", saying she could not under laws governing the public service.

She said former Commonwealth ombudsman, acting NSW ombudsman and Australian information commissioner John McMillan was continuing an inquiry into a complaint lodged in December about Mr Lloyd. Mr Davidson launched the investigation in June upon the recommendation of an independent former public service leader.

Ms Waugh said Professor McMillan would report to her once he had finished the inquiry, and she would tell the Senate president and House of Representatives speaker its results.

"I cannot provide any further comment except to say that I will conclude the matter as quickly as possible," she said.

The Australian Public Service Commission also declined to comment.

Investigations into the complaints may remain unfinished when Mr Lloyd leaves his $706,000-a-year role on August 8, after he announced in June he would resign.

Under public service legislation there is no power to investigate Mr Lloyd, who is responsible for upholding standards of integrity and conduct in the Australian Public Service, once he departs the agency.

Mr Lloyd, a member of the Institute of Public Affairs, wrote an email on October 24 titled "PR for IPA" to its head John Roskam after Labor senators in an estimates hearing the day before questioned his communications with the think tank.

"More publicity for the IPA, including page one of Canberra Times, thanks to ALP questioning in estimates yesterday," Mr Lloyd wrote.

The complaint sent to the merit protection commissioner in June followed another made to the Department of Prime Minister and Cabinet in December, and received by Mr Davidson the next month.

Mr Davidson intially didn't act on the December complaint, believing the merit protection commissioner role would be filled permanently within weeks. When a permanent merit protection commissioner was not appointed by March, he said he dealt with his conflict of interest by contracting former Attorney-General's Department secretary Robert Cornall to advise on whether to commence an inquiry.

The allegation raised in the first complaint has not been described publicly.

Mr Lloyd, whose term was due to expire in December 2019, abruptly announced last month he would resign but denied the timing was influenced by a possible investigation. His agency said then he had "for some time" considered departing before his term as commissioner ended, and Mr Lloyd later told senators he had felt it was time to resign after a long career.

His announcement came after mounting pressure over his connection to the IPA, and revelations in May he faced a possible inquiry.

Mr Lloyd's links to the think tank came under growing scrutiny after it was revealed at a Senate estimates hearing in October he sent an email to a member of the IPA with an attachment showing what he described as "generous" provisions in public service enterprise agreements.

He has rejected suggestions he gave it special access and research.