Lerner announced his intention to sell the club last week, casting doubt over the position of Lambert if and when a new owner is found.
However, after returning from a trip to the United States alongside chief executive Paul Faulkner, Lambert underlined his wish to remain in his post and take the club forward.
"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," he 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.
"I'm determined to give it everything I have, the players will do the same and it is our collective strength as a club which, ultimately, will see us through."
