Bayern scraped past CONCACAF champion Tigres UANL 1-0 in Qatar to clinch its second Club World Cup title.
It marked the sixth trophy Bayern has won in Hansi Flick's tenure, with that list also including last season's Bundesliga, DFB-Pokal and Champions League and this season's UEFA Super Cup and DFL-Supercup.
Lewandowski, who scooped The Best FIFA Men's Player award for 2020, has been integral and played a key part in Bayern's win over Tigres as he forced Nahuel Guzman to flap at a cross, allowing Benjamin Pavard to lash in the decisive goal.
"The six-pack is something special, a great story – not only for Bayern Munich, for all of football," Lewandowski said. "The way we played, that will stay for a long, long time."
Bayern is the first team since Pep Guardiola's Barcelona, in 2009, to complete a clean sweep of every trophy on offer.
"Congratulations to my team, they have achieved something historic with their sixth title," Flick said. "This is also the best season for the successful Bayern. There was a lot of unrest in the last few days but they still played outstandingly well.
"We are all very, very proud of the team. It is outstanding what they have achieved."
Bayern had to overcome Tigres without a handful of key players; Javi Martinez and Leon Goretzka did not travel to Qatar as they recover from COVID-19, with Thomas Muller then returning a positive result, while Jerome Boateng has had to return to Germany for personal reasons.
Bayern's performance was unconvincing at times, but it ultimately had the quality to get through, with Tigres only managing one attempt on target and failing to muster a single effort after half-time.
Joshua Kimmich turned in another star performance in the centre of the park, having a stunning goal harshly disallowed and creating a game-high four chances, but the Germany maestro regretted that Muller – who is isolating – was unable to take part.
"It was bitter for Thomas Muller that he wasn't there," Kimmich said. "We also got the win for him and all the others who couldn't be with us."