Lambert admitted after Villa's 4-0 defeat at Manchester City on Wednesday that he was very much in the dark about whether or not Lerner intends to sell the club.
Reports in the British press claimed Lerner was looking to part company with Villa, casting doubt on Lambert's future in the process.
Lerner responded to the speculation by releasing a statement in which he confirmed that he will clarify his own position at the end of the season and Lambert has no desire to follow the American out of Villa if he does decide to sell up.
After the 3-0 loss at Tottenham on the final day of the Premier League campaign on Sunday, Lambert told BBC Sport: "What is going to happen next week will happen. It's a great club and it shouldn't be where it is (15th).
"I'm the manager of the club and hope to still be here. It's plain to see what we need. If you don't get investment, then it is always hard.
"It's a massive club and the lads are hurting with the criticism but, as I said to the lads, they should be proud for staying up because it's a hell of an achievement."
In his post-match press conference at White Hart Lane, Lambert acknowledged that this season has been tough, with uncertainty in the boardroom, injuries to key players and the club's fans voicing their frustrations contributing to a turbulent last 12 months.
However, Lambert believes guiding Villa to safety in such circumstances is his greatest achievement as a manager.
He added: "It's probably the greatest thing I've done since being a manager and I'm saying that after successive promotions with Norwich.
"But the magnitude of this club with everything that has been going on, it’s been really tough.
"But I said to the lads then (after the match), they've nothing to be ashamed of. It will make them stronger.
"When you come through adversity it makes you stronger."
