Lambert took charge at Villa in the summer of 2012 as a replacement for Alex McLeish and in his first season in they found themselves embroiled in a relegation for most of the campaign.
Former Norwich chief Lambert admits Lerner could have panicked and sacked him following some indifferent results, but he feels Villa have now turned the corner.
"I remember Randy saying to me, 'Paul this will be your hardest year in football' and he was right. It was tough, really hard," Lambert told the Sun on Sunday.
"But we stuck to our beliefs and the crowd were great, even though we were getting beaten - sometimes pretty heavily. The supporters could have turned on me but they were excellent.
"Some owners would have got rid of me, I know that. They would have panicked and gone, 'Boom, you're out. Thankfully, I have had a good relationship with Randy and Paul Faulkner, the chief executive.
"Also the players never wavered, even though we had that bad spell. They had the belief we would go and do it.
"After January, it gradually got better. We kept trying to be upbeat.
"The supporters could have had a big say as they may have driven me out of the club. I am thankful for that, even through the tough times.
"The difference now is a big turnaround from what has happened. You need to take a step backwards to go forward and I think that is what has happened.
"We have progressed after a tough start to the season. There is a good spirit, which will take you a long way."