On 25 February 2014, Lewandowski scored twice in Champions League round-of-16 first-leg against Zenit Saint Petersburg, becoming BVB's overall top scorer in European competition, surpassing Stéphane Chapuisat's 16 goals record. He scored his 100th goal for the club on his 182nd appearance, as Dortmund defeated VfL Wolfsburg in the semi-finals of the DFB-Pokal on 16 April 2014, and revealed a shirt with the number 100 in celebration.
Lewandowski played his final match for Dortmund in the 2014 German Cup final against Bayern Munich on 17 May. Manager Jürgen Klopp had excused him from some training ahead of the final due to injury concerns; although Lewandowski played all 120 minutes of the final, Dortmund lost 2–0. He finished the season with 28 goals in 48 matches.
Pre-season started on 9 July 2014 at which time he was presented. He made his pre–season debut on 21 July 2014, scoring a goal in the process. On 6 August, he opened the scoring as Bayern contested the 2014 MLS All-Star Game in Portland, Oregon, eventually losing 1–2.
He made his competitive debut for his new club in a 2–0 loss to Borussia Dortmund in the 2014 German Super Cup on 13 August 2014, and scored his first goal in a 1–1 draw against Schalke 04 in his second league match on 30 August. On 21 October, Lewandowski scored his first Champions League goal with Bayern Munich in a 7–1 away win against A.S. Roma. On 1 November, in his first league match against Dortmund, Lewandowski scored in a 2–1 win which put Bayern four points clear at the top of the table while leaving his former club in a relegation play-off place. In his third match of the season against Dortmund on 4 April 2015, Lewandowski scored in the 36th minute in a 1–0 win. He had scored after Roman Weidenfeller "parried" Thomas Müller's shot.
On 7 September 2014, in Poland's first UEFA Euro 2016 qualifier, away against Gibraltar, Lewandowski scored his first international hat-trick, netting four goals in a 7–0 win. On 13 June 2015, he scored another hat-trick in Poland's 4–0 defeat of Georgia, with the three goals scored within the space of four minutes. On 8 October, he scored twice in a 2–2 draw away to Scotland, opening and equalising with the last kick of the game to eliminate the hosts. Three days later he headed the winner in a 2–1 victory against the Republic of Ireland, qualifying Poland for the tournament finals in France. Lewandowski ended the campaign with 13 goals, a joint European Championships qualifying record with David Healy's tally for Northern Ireland in UEFA Euro 2008 qualifying.
Lewandowski is a practising Catholic. He met Pope Francis in October 2014, when Bayern Munich visited Vatican City following a 7–1 win over A.S. Roma in the UEFA Champions League.
In March 2014, he was named a UNICEF Goodwill Ambassador.