Lambert won the Champions League 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."