Drusilla Sharpling, a member of the probe's panel, said she reported concerns to a director general at the department at the end of April - but stressed she did not require any action to be taken, or give permission to "spread" the concerns.
Dame Lowell, a former New Zealand high court judge, resigned as chairwoman in August this year - saying there had been a "legacy of failure which has been very hard to shake off".
Last week, Dame Lowell strongly denied published allegations against her, describing them as "falsities", "malicious" and part of a "vicious campaign".
Ms Sharpling told the Commons Home Affairs committee the panel "had concerns about the qualities of leadership that were being evidenced".
"At the end of April, with the panel's knowledge, I reported my concerns about the leadership of the inquiry to the then director general of the Home Office, Mary Calam.
"I did not give anyone permission to spread these concerns amongst anybody else, that I did not, and neither did the panel, require any action to be taken."
Ivor Frank, another member of the panel, said there were "challenges" during Dame Lowell's 16 months as chairwoman as she was not always in the UK.
She spent more than 70 days working abroad or on holiday during her time in charge.
"There were times when things were perfectly amicable and perfectly professional. There were other times when it was less the case," Mr Frank said.
Later Mark Sedwill, permanent secretary at the Home Office, said he was not aware of Ms Sharpling's meeting in April.
He also said that no complaint had been made against Dame Lowell.
- NZN/AAP
