Lewandowski was officially confirmed as a Bayern player in July after signing a pre-contract agreement with the Bavarian club in January.
The move ended the Poland international's prolific four-year spell with Borussia Dortmund, who Bayern will face in the DFL Supercup in 10 days' time.
The 25-year-old netted 103 goals in his time at Signal Iduna Park, but feels he can make further strides with Pep Guardiola's men.
"I know I can get even better. It doesn't matter where you've played and what you've won, you always have to give it everything you've got," Lewandowski said.
"[I am] not yet at the limit. I hope I can get better every day."
Bayern's stars from Germany's successful World Cup campaign will return to the squad for their last friendly clash with an MLS All-Star team at Providence Park in Portland on Wednesday, just a week before the Supercup clash with Dortmund.
The Supercup is to be held at Signal Iduna Park, and, while Lewandowski is relishing the occasion, he expects his first competitive match as a Bayern player to be a challenging one.
"It's obviously going to be special for me," he added. "I had four fantastic years there [Dortmund], but it'll feel very different as a member of the visiting team.
"[It will be] a difficult evening, simply because we'll only have trained together for a week. But we're a good team and we'll obviously play to win."
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