Lapadula was born in Turin on 7 February 1990, to Gianfranco Lapadula from the region of Apulia and Blanca Aida Vargas Higinio from Peru. He has a brother named David who was also a forward, in the lower amateur leagues.

Lapadula began his career with Juventus before releasing in 2004 because he was not doing well in his studies. After that he moved to Collegno Paradiso, then left on loan to Treviso in 2006. He returned to Piedmont for Serie C2 side Pro Vercelli on 31 August 2007. He was a player of the reserve. In 2008–09 season, he left for Lega Pro Seconda Divisione (ex–Serie C2) side Ivrea, and was selected to the Lega Pro 2nd Div. A representative team for Lega Pro Quadrangular Tournament and scored a goal against 2nd Div. C representative team in the third place match. Eventually, Group A finished as the third. In August 2009 he was signed by Parma and spent one season with their Primavera team. In July 2010 left for Atletico Roma.

Lapadula made his debut for Atletico Roma on 8 August 2010, in the Coppa Italia preliminary round, lost in extra time (1–2). In January 2011, he left for Ravenna. He concluded the 2011–12 season as the topscorer in Group A with 24 goals.

On 15 June 2012, Lapadula joined Serie B club Cesena in co-ownership, signing a five-year contract. Lapadula failed to play regularly for Cesena, and on 8 January 2013 he was signed by Frosinone. In July 2013 the co-ownership between Cesena and Parma was resolved, and Lapadula returned to Parma.

In July 2014 he was loaned to Teramo, where he scored 21 goals and helped the club achieve promotion to Serie B, then cancelled in August 2015 by the final judgment of the Italian Football Federation, due to match-fixing on the part of the President of Teramo, Luciano Campitellii, in the penultimate round of the league in the match against Savona.

After the bankruptcy of Parma Lapadula was released on a free transfer, and in July 2015 he was signed by Pescara in Serie B on a four-year contract. In the 2015–16 season he scored 30 goals in 43 appearances (including three goals in as many appearances in the playoffs), without scoring any penalties, earning the honour of top scorer in the Italian second division.

On 24 June 2016, Lapadula passed his medical test with A.C. Milan, who reportedly paid Pescara €9 million plus bonus for the transfer, while the player signed a five-year deal. He made his debut for Milan on 27 August 2016, coming on as an 86th-minute substitute during a 4–2 loss away against Napoli in Serie A. He scored his first goal for Milan and in Serie A on 6 November 2016 in the 2–1 away victory against Palermo, three minutes after coming on as a substitute for Carlos Bacca. On 26 November, Lapadula scored his first brace in Serie A in a 1–4 away victory against Empoli. He finished the 2016–17 season with 8 goals in 27 games, two of which were scored from a penalty spot.

Due to his family heritage Lapadula is eligible to play for Italy and Peru. He had received a call-up by Peru for the Copa América Centenario but had not officially decided which international side to represent. On 7 November 2016, he was called up to the Italy senior squad for the first time for a 2018 FIFA World Cup Qualification match against Liechtenstein and a friendly match against Germany, replacing the injured Napoli forward Manolo Gabbiadini.

On 18 July 2017, Lapadula moved to Genoa, on a one-season loan with an obligation to make the deal permanent. The total transfer fee was €13 million (€2 million loan + €11 million for outright) which was Genoa’s most expensive signing of all-time.

On 31 May 2017, Lapadula scored a hat-trick for Italy national football B team in a friendly against San Marino.

On 12 July 2019, he was loaned to Serie A newcomers Lecce.

On 2 September 2020, Lapadula signed with Benevento 3-years contract.

On 30 October 2020, Lapadula was called-up by Ricardo Gareca to the Peru senior team for 2022 FIFA World Cup qualification matches against Chile and Argentina. He made his debut on 13 November 2020, as a substitute in the match against Chile.