Lewandowski netted for the 41st and 42nd time in 2021 with his brace in the 5-0 victory at VfB Stuttgart on Matchday 16 - just his 33rd game of the year.
The 33-year-old has one more chance to claim the record outright when Bayern host Wolfsburg on Matchday 17. He already has 23 Bundesliga goals to his name against the Wolves - including five in nine minutes - which is the most he has against any team in the league.
The Bundesliga's record goalscorer with 365, Müller got his 42 across 34 games in 1972. That spanned the famous 1971/72 campaign where Der Bomber netted his once record-setting 40 goals in a season.
That historic total also fell to the reigning Best FIFA Men's Player and European Golden Shoe winner in 2020/21, with Lewandowski bringing up his 41st goal with the final kick of the campaign.
The incumbent No.9 in Munich is now only 70 goals behind Müller's all-time total, which he could just reach - at his current rate - before his contract expires at the end of 2022/23.
Before then, he could claim the Bundesliga record for most games in which he's scored. That is currently held by Müller (228) - and Klaus Fischer is also still ahead on 209 - but the Stuttgart match was Lewandowski's 201st in the Bundesliga with a goal.
His 200th - the Klassiker victory at former club Borussia Dortmund - already saw him break the record for most away goals in the Bundesliga, scoring another brace to move onto 118 and past Fischer's previous best of 117. He's now on 120 after his latest two-goal haul in Stuttgart.