Heynckes returned for a fourth spell in charge of the record Bundesliga champions earlier this month following Carlo Ancelotti's removal that came on the back of a demoralising 3-0 UEFA Champions League defeat to Paris Saint-Germain.
Watch: The history of Jupp Heynckes - Bayern Munich's go-to man
After seeing Bayern sweep Freiburg aside 5-0 on Matchday 8 — his first game back — Heynckes is now preparing to face Lambert's former club Celtic on Wednesday in his opening European match since winning the Champions League in 2012/13.
That victory over Dortmund at Wembley completed an unprecedented treble, and Lambert believes the Bavarian giants will enjoy success under the veteran tactician once again.
"He's the last guy to do the treble, which not many people do here," Lambert, who helped Dortmund reach the summit of European football in 1996/97, told BBC Scotland. "The players know him, so I think it's a clever move from the club."
Lambert, who played just a single season with BVB before turning out for Celtic for eight years, has been in Germany this week studying coaching methods and has been impressed with Bayern at close quarters.
"I watched them train this week and went to their game [against Freiburg] — they were brilliant, absolutely outstanding. I saw them training and when I came out from training I thought 'they've got their tails up again'. It looked like that," the former Norwich City and Aston Villa manager said.
"Their build-up play from the back, they probably have two of the best centre-halves in Europe that can play with the ball from the back. They have a young kid at right back, [Joshua] Kimmich, who was outstanding yesterday. They have [David] Alaba on the left who flies up and down the side. They were excellent."
Like Lambert, Celtic boss Brendan Rodgers will have seen Bayern's dismissal of Freiburg in what was arguably their most impressive performance this season.
Having lost ground to PSG on Matchday 2, Bayern will be doubly determined to triumph at the Allianz Arena, leaving Celtic — 3-0 winners over Anderlecht in their last European outing — facing a huge challenge if they are not to leave empty-handed.
Watch: Bayern's perfect treble-winning 2012/13 season!
"You have a chance in any football match, but Bayern Munich have to be off the pace," said Lambert. "Celtic will know themselves, you don't come to the Allianz Arena and think you can play your normal game - you have to raise it. Their crowd is vibrant, they move the ball really quickly and they have incredible technical footballers there.
"Celtic have a chance if they play above themselves and don't give Bayern Munich respect - you have to go up against them, you can't let them play."