Villa face another crunch clash in their battle to avoid relegation from the Barclays Premier League when they meet fellow strugglers Sunderland at Villa Park on Monday.
Lambert's former club Dortmund have rather loftier ambitions as they bid to turn a 4-1 first-leg advantage over Real Madrid into a place in the Champions League final.
Lambert won the trophy with the German side in 1997 and knows Villa, former winners themselves, aspire to greater things but has been heartened by the way the club have pulled together.
He said: "The crowd have been fantastic. It's like the Dortmund crowd at the minute. It's the exact same when I was there. You give it everything you've got and they will respond that way.
"What makes that one is the fact the lads have come through the youth. The crowd have identified that. They are right behind it. That's what you try to do here.
"I think a lot of people could have turned away. But the crowd have been fantastic, they have stayed with us. It's a club with history and tradition. They have won big things here. Any team that has won a European Cup, there's always pressure there."
Lambert has long been a cheerleader for the Bundesliga and is still in touch with people at Dortmund.
The Scot studied for his coaching qualifications in Germany alongside Dortmund boss Jurgen Klopp, who has emerged as one of the brightest managerial talents in Europe despite not being a star pupil, according to Lambert.
He said: "I did the licence over there. It was a great experience. It was a long time ago now. That and playing abroad was probably one of the hardest things I've done because of the timescale and the newness of it.
"It's totally different - the magnitude of what you have to learn and the fact you had exams after it. I don't care what age you are, if someone says you've got exams after a course, you tend to think, 'Oh no, you could fail this.'
"Jurgen Klopp came on the last six months and he did average. He was trainer at Mainz when he was there. He was just finishing it off. He was there for the last bit. He's a good guy and I'm absolutely delighted he's doing great as he's doing."
Klopp and Lambert may find themselves in a similar position at the end of the season as they bid to hold on to their young players.
Dortmund have already agreed a fee with Bayern Munich for playmaker Mario Gotze and will have to fend off interest in star striker Robert Lewandowski.
Villa are likely to have offers for striker Christian Benteke while defender Matthew Lowton has this week been linked with Fulham and Arsenal.
Lambert said: "I think that's when it becomes frustrating, if you do have to lose ones because you're trying to build. Dortmund are going through the same with Mario Gotze going to Bayern.
"Maybe the big lad up front (Lewandowski) might go. You just hope you keep building. If not, you have to go and get ones the same. If you're building something like that, you want to try and see it through.
"At the end of the day, the decision is my own if I let people go. That would always be the case. There's no point trying to plan something, thinking it's going to grow and then all of a sudden it's not there. You have to let it build."