The ever shrinking investment from Lerner, who bought a 60 percent stake in the club at the start of the 2006/07 season, has led to the speculation the American will sell up after the final league matches at Manchester City and Tottenham Hotspur this week.
New owners often mean new managers but former Borussia Dortmund midfielder Lambert was hopeful he could be allowed a third season at the helm.
“I hope so, that is what I want to do,” Lambert was quoted as saying by British media on Monday.
“But you’ll know when the chairman says what he is going to do. You would love to do it, it is a fantastic club, albeit the last couple of years has been tough.
“I think the chairman has said himself I have had to work within the parameters he has set between me and him. You either take the challenge on or bottle it.”
Having recorded a 1-0 win over title chasing Chelsea in March, Villa plummeted down the table with only one point from six matches to join the relegation battle.
With tough fixtures at City and Spurs to finish, Saturday’s clash at home to Hull came with huge pressure but Ashley Westwood put them ahead inside a minute and Andreas Weimann scored twice to claim a priceless three points.
The win moved them up to 14th on 38 points, five clear of 18th-placed Norwich City who only have one match left at home to Arsenal, and Lambert did not hide his sense of relief.
“That’s an understatement,” the Scot said. “I have been involved in massive games but that is too close for comfort.”
After Villa held Southampton to a 0-0 draw at home last month, Lerner released a statement urging fans to get behind the team and gave praise to Lambert.
The 52-year-old, who used to own the NFL’s Cleveland Browns franchise, also acknowledged the rumours of his departure but failed to quash them and said all would be revealed at the end of the season.
With matters on the field finalised and another season in the lucrative league assured, attentions switch back to the American with Lambert left pondering a possible exit.
“I respect the chairman’s statement and what he is going to say,” he said. “It will bring clarity and it will not be a problem, whatever way he wants to play it himself.
“I will respect his decision, no problem with that whatsoever. Randy is a really top guy and I’ve said before, it is his club.”
(Writing by Patrick Johnston, editing by Nick Mulvenney)