Lambert hopes for Villa stay next season
Villa have battled in the bottom half of the Premier League table this season, even flirting with relegation in recent weeks following six games without a win.
Last Saturday's 3-1 win over Hull City allayed any fears of dropping out of the top flight, but Lambert believes things need to change if the club are to improve next season.
"I really don't know (what my future is)," Lambert told Sky Sports. "What he's (Lerner) going to say in the next six or seven days, I really don't know.
"This club has got to be stronger. It's too big a club. I would love to be (in charge). It's a brilliant club with a fabulous fan base.
"Any club that wins a European Cup creates history and tradition and this club has got it in abundance.
"This team has got to live up to it (the tradition) and at the minute we haven't done it."