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.
"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."
