Before conquering Bavaria, Lewandowski was Dortmund's main man under Klopp for four years.
During his time at Signal Iduna Park, Lewandowski scored more than 100 goals in all competitions before joining Bayern in 2014 and the Poland international thanks Klopp - now in charge of Liverpool - for making him a better striker.
"He was the one who gave me belief," Lewandowski told the Daily Mail.
"In the first three or four months in training, we would have this game — him against the striker. There would be a bet between me and him.
"In the first few training sessions, he was always winning! After that, not so much! Every time after, he lost! He didn't want to play anymore! It was €50 a game and by the end I had a positive balance! But I saw for the first time with him how important it was [to] train.
"I saw what I have to do on the pitch when I don't have the ball. You look at Liverpool now and how they play with the pressing. That is what I learned from him.
"He also improved my finishing. When I came to Dortmund, it wasn't so good. He told me to improve. He showed me what I had to do."
This season, Lewandowski has scored 15 Bundesliga goals to help Bayern top the standings after 19 matches.
Lewandowski and Bayern travel to Ingolstadt on Saturday.