The Polish striker pounced on a poorly judged back pass after nine minutes to steer in his 72nd goal in the competition.
In doing so, he surpassed former Real Madrid striker Raul in the competition scoring charts to reach a total only bettered by Juventus’ Cristiano Ronaldo, with 134 goals, and Barcelona’s Lionel Messi, with 119.
Bayerns 17-year-old midfielder Jamal Musiala doubled their advantage with a well-taken strike that made him the youngest English player to score in the competition.
Leroy Sane tapped in a third before the break and a Francesco Acerbi own goal stretched the visitors’ advantage early in the second half, but Joaquin Correa soon pulled one back for Lazio, whose unbeaten run in the competition came crashing to an end.
It was an 18th consecutive match without defeat for Bayern in the Champions League, 17 of which have been victories, leaving the German champions in a dominant position ahead of the second leg in Munich on March 17.
Bayern came into the game with a point to prove after earning one point from two league games since winning the Club World Cup earlier this month.
They soon demonstrated their pedigree against a Lazio side competing in its first Champions League knockout match since 1999.
Lewandowski anticipated a loose pass from Mateo Musacchio and rounded Pepe Reina to tap in, but Lazio were furious when penalty claims were waved away after Sergej Milinkovic-Savic was felled in the box.
England Under-21 international Musiala, who is also eligible to play for Germany, fired into the bottom corner after 24 minutes.
Bayern then put the contest beyond doubt when Sane tapped in from a Reina parry and Acerbi diverted a cross into his own net either side of the break.
Lazio produced chances of their own, finishing the game with 14 attempts to Bayern’s 13, but Correa’s weaving run and finish was their only successful effort.
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