However, after holding talks with Lerner and chief executive Paul Faulkner in New York, the Scot is eager to remain in charge of the team.
"As everybody is aware, I met with the chairman along with Paul and I'm determined to get on with the job of managing Aston Villa," Lambert told the club's official website.
"These circumstances are extremely challenging as the club is for sale and as far as I know there is nothing imminent in terms of new ownership, but we're going to roll up our sleeves, prepare for the battle ahead and do our best by the club.
"The squad requires strengthening, that's self-evident, and it won't be easy within the current circumstances. But we'll look to identify players of proven quality to bring in and get ready for the start of the new season."
Villa finished in 15th place in the Premier League table last season, five points above the relegation zone.