Bayern dropped their first points of the season in their previous match, a draw against Cologne, following five straight wins.
That came just days after their first loss of the season, against Atletico Madrid in the Champions League.
"What is clear is that we need to improve if we are to challenge for all titles," Lahm said.
"We must improve our aggressiveness because that has been our trademark in the past few years, to show the opponent they cannot get anything against us. We need to do that better."
Few, however, will be betting against a record-extending fifth straight Bundesliga title, with Arjen Robben and Franck Ribery also gradually hitting top form after injury breaks.
Especially 33-year-old French winger Ribery, fighting for a contract renewal, has enjoyed a fine start to the season, having scored twice and set up another five goals in the league.
"They are both showing what quality they have," Lahm said of the pair, nicknamed "Robbery".
"They have the experience and have been playing at top level for years. They are winners."
Bayern are three points clear of second-placed Hertha Berlin, and four ahead of main title rivals Borussia Dortmund, who take on the in-form Berliners on Friday.
Dortmund are looking to recover from their defeat to Bayer Leverkusen but efficient Hertha have shot out of the blocks with four wins in six games to climb to second place, despite scoring less and conceding more goals than the Ruhr valley club.
"It looks very good at the moment but it is not that suddenly those become our expectations," Hertha's Swiss international Valentin Stocker said.
"We know that this can turn very quickly, just like two years ago when we were almost relegated. So we have to stay humble.
"Dortmund will be stepping wildly on the gas pedal against us because they are desperate to win after their loss. But we always have a good game play and hope we can execute it well again on Friday."
At the other end of the table former European champions Hamburg SV will be hoping their first win of the season will come at Champions League club Borussia Moenchengladbach to lift them off last place in the Bundesliga.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
