Speculation that Lerner will look to sell the club this summer has been growing since he released a vague statement last month which indicated only that he would clarify his own position at the end of the season.
With Barclays Premier League football now virtually assured following the 3-1 victory at Villa Park, all eyes are on the American businessman's next move.
But Lambert, whose own future is uncertain as a result of perceived instability at the top, has no inside track.
Asked what developments he expected at boardroom level, the Scot said: "You're asking me a question I can't give an answer to and that's me being honest.
"The chairman will come out and say what he's going to say and I really don't know what he will say. His statement is what it is. I understand what has gone on in the last few weeks and I'm pretty sure people will find out soon."
Lambert was more comfortable reflecting on footballing matters, with a first win in seven matches delivered by Ashley Westwood's opener inside the first minute and a pair of headers from Andreas Weimann.
Pressure had been mounting by the week and Lambert was pleased to see the response he wanted both on and off the field.
"The crowd was excellent," he said.
"I think people were probably thinking there would be some animosity towards myself - and if that happens you've got to accept it - but the start we got put everybody in a good frame of mind.
"This game was huge. I've been involved in some massive games before, but the pressure on this one was incredible.
"They came through it and if they came through that they can come through everything in their careers.
"I thought they were outstanding and we deserved to win."
Hull boss Steve Bruce, whose side slipped below Villa and into 15th place after their third successive game without a win, admitted FA Cup final fever has had an effect on his side.
Attention in East Yorkshire has been focused firmly on the May 17 trip to Wembley since last month's semi-final success over Sheffield United, but Bruce has been battling hard to keep his players on the task at hand.
As yet, it is a battle he has been losing.
"I've said for the last couple of weeks we have to keep focused," he said.
"The whole city is talking about the FA Cup final and why shouldn't it be? But it's been very, very difficult to keep a lid on it when we've still got a little bit of work to do.
"It's at the forefront of everybody's mind and that's only human nature because it's something we're all looking forward to.
"But we didn't do enough to win this game. We were so sloppy, awful in our defending.
"We didn't get started and didn't show that resilience you need to win a game or draw a game in the Premier League."
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