He stood out in indoor soccer football divisions, demonstrating his capabilities in the class of 1993 of the Club Academia Kaly de Ituzaingó, a neighbourhood club. Ramón Maddoni, who discovered players like Juan Román Riquelme, Carlos Tevez and Esteban Cambiasso, wanted to take him to Boca Juniors for a test match but the young Lanzini firmly declined the call, stating that he only aimed to play for the club that he supported: Club Atlético River Plate. He was finally taken to River Plate, in 2002. He began playing as a playmaker in junior divisions. Lanzini began training in River and, after several tests, Pedro Vega, ex player and coach of inferior divisions from the club, ordered to hire him. In 2008 the 8th division team of which he was a part of won the trophy for that division, with a personal mark of 9 goals, only 2 less than Leonardo Salguero, who was his companion in attack and top scorer of the team with 11 goals. On 2 November 2008, River Plate won the junior division’s Superclásico 3–0 to Boca Juniors with Lanzini scoring 2 goals and assisting the mentioned Salguero in other.

In 2010, the coach of River Plate’s first team Ángel Cappa, included him in the team for the winter preseason, disputing several matches in Salta Province. He then made his informal debut in a friendly match against Central Norte, a 3–0 victory, coming on as a second-half substitute for Ariel Ortega. He then played another friendly match against Juventud Antoniana, in which his performance obtained a very good reception from the press and fans alike.

The mentioned performances in 2010 winter’s preseason satisfied the coach. Finally he made his first appearance on 8 August 2010, against Tigre for the first match of the Torneo Apertura 2010. River won 1–0 and Lanzini was replaced at half time by Facundo Affranchino.

19 July 2011 an agreement was reached between River Plate and Fluminense, with the latter taking the player on loan for a fee of US$400,000, with a transfer option of €15,000,000.

Things would be different for the club in 2014. That year proved to be one of the most memorable year’s in club’s history, winning the Torneo Final 2014 and the Copa Sudamericana 2014 kicking out Boca Juniors from that international competition. Lanzini remained half of the year as part of the team, so he was part of the Torneo Inicial 2014 trophy; during that time he continued to be one of the most important players in the pitch. He had the honor to once again score a goal in the team’s victory in the 2014 Superclásico against Boca Juniors, the so-called “Bombonerazo” which began a series of crushing victories of River Plate over Boca Juniors. This match stood out in particular because it was the one that definitively launched the career of his teammate Ramiro Funes Mori, a defender who scored a header in the last minutes of the match; he would end up also playing in the Premier League, as Lanzini, for Everton FC. River Plate would end up being Torneo Final 2014 champion, with a very solid performance from Manu, who scored 2 goals in 18 appearances.

In 2014 Lanzini became the youngest foreign player, at 21, to play in the UAE Arabian Gulf League when he signed a four-year deal for Al Jazira Club. He had been courted by clubs in England, Spain, Italy and Turkey, and was signed as a replacement for Marseille-bound Abdelaziz Barrada.

On 22 July 2015, Lanzini signed for Premier League side West Ham United on a season-long loan, with an option to make the move permanent. He made his debut on 6 August in the UEFA Europa League third qualifying round away to Astra Giurgiu, starting the match and scoring in the third minute, however the Hammers lost 2–1 (4–3 on aggregate) and were eliminated. His league debut came on 15 August as a 76th-minute substitute for Cheikhou Kouyaté in a 1–2 home defeat to Leicester City. On 29 August, he scored his first league goal after just three minutes away to Liverpool, and assisted a Mark Noble goal as the Hammers won 3–0 for their first victory at Anfield since 1963. In March 2016, West Ham confirmed that they had taken up the option to sign Lanzini on a permanent deal, with effect from 1 July 2016.

Lanzini played 39 games in all competitions for West Ham, scoring eight goals. On 15 October 2016 he scored the only goal in a 1–0 win away to Crystal Palace to give West Ham their first away win on the season. His goal in a 1–0 win against Tottenham Hotspur on 5 May 2017 halted Tottenham’s challenge to win the Premier League title. Tottenham, at the time, were on a nine-match winning run and were challenging Chelsea for the league title. On 9 May he was voted runner-up to Michail Antonio as Hammer of the Year and the Players’ Player of the Year.

In May 2016, Lanzini was named in Argentina’s provisional 35-man squad for the 2016 Olympics in Rio de Janeiro. He withdrew from the squad in July 2016 following a knee injury sustained while training in Miami, Florida, returning to London for treatment with West Ham United. In May 2017 Lanzini was named in new Argentina manager Jorge Sampaoli’s first squad for the upcoming friendlies against Brazil and Singapore, with Lanzini making his full international debut on 9 June against Brazil at the MCG in Melbourne, Australia, replacing Ever Banega in the 81st minute of La Albiceleste’s 1–0 win. On 23 March 2018 he played a friendly match against Italy at Etihad Stadium in Manchester and scored his first international goal, as Argentina secured a 2–0 victory.

Lanzini made his first appearance of the season on 26 August 2017, in a 3–0 defeat away at Newcastle United. In the same game, Lanzini was caught with an elbow by Aleksandar Mitrović, who was later banned for three games as a result of the incident. Lanzini scored his first goal of the season in a 1–4 defeat at home to Liverpool on 4 November 2017, before adding a further two goals to his tally on 13 January 2018 in a 4–1 away win at Huddersfield Town. On 13 May, he scored twice in a 3–1 win over Everton, on the final day of the season.

On 21 May 2018 he was named in Argentina’s final 23-man squad for the 2018 FIFA World Cup in Russia, and started in the 4–0 friendly win against Haiti on 29 May in Buenos Aires, playing an hour before being substituted for Maximiliano Meza. On 8 June 2018, Lanzini was ruled out of the World Cup after suffering a ruptured anterior knee ligament injury during the training session.

After being sidelined due to injury since May 2018, Lanzini made his first appearance of the season on 22 February 2019, coming on as a 76th minute substitute for Felipe Anderson in a 3–1 home win against Fulham F.C..

Lanzini made his first appearance of the season on 10 August 2019 in West Ham’s opening game against 2018/2019 Premier League Champions, Manchester City, resulting in a 5–0 loss. Following Lanzini making his 100th Premier League appearance, it was announced on 30 August 2019 that Lanzini had signed a new long-term contract with West Ham, extending his contract till 30 June 2023, with Lanzini stating “I love London, I love the Club, I am happy here, we have a very good team, we have a very good manager and the Club wants to change and to be in more competitions in the future and that’s good for us”. On 9 November, Lanzini suffered a broken collarbone during the closing stages of a 3–0 defeat by Burnley.

On 18 October 2020, in his first league game of the season, Lanzini scored his first goal of the season, in a 3-3 away draw against Tottenham Hotspur. Trailing 3-0 until the 82nd minute, Lanzini scored in the fourth minute of added time to make the score 3-3. West Ham became the first team in the history of the Premier League to avoid defeat having been losing by three or more goals as late in the game as the 81st minute.