The Bavarian giants finished this year's Bundesliga campaign on top with a 26-point advantage over Jurgen Klopp's side, having lost out to BVB in the title race in the previous two seasons.
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"The team is hungry, as we've seen throughout the season," the 29-year-old told Fifa.com.
"We refused to be distracted by our huge lead [in the Bundesliga], nor by losing last season's Champions League final.
"We've stuck to our course, and we'll continue on it. We're hoping to win the treble, and I'm very confident. This team could be very successful over the next few years, both at home and in Europe."
Should Jupp Heynckes team be successful against BVB, they will have the opportunity to clinch an historic treble when they face Stuttgart in the DFB-Pokal final on June 1, and Lahm has urged his team-mates to go all out for success as the season draws to a close.
"If we win this trophy, I want us to go on and win the German cup a week later," he added.