At age of 12, Lee caught the attention of FC Barcelona after he finished as the top scorer in the 2010 Danone Nations Cup, one of the most prestigious youth football tournaments. He joined Barcelona’s youth academy, La Masia, and scored 39 goals in 29 appearances during his first season. He was also named the best player in four youth tournaments: Torneo Canillas, Memorial Gaetano Scirea, Trofeo San Bonifacio and Gabala Cup; and was nicknamed the “Korean Messi”. However, he was banned from playing in the regular season for three years until his 18th birthday by transfer regulations of FIFA. On 13 March 2016, he made his senior debut for the B team.

Lee made his international debut as a part of South Korea under-16 team competing for the 2014 AFC U-16 Championship qualification. He scored four goals against Laos. In April 2014, he participated in the Montaigu Tournament with South Korea under-16 team, and they finished the tournament as runners-up after he scored two goals.

At the 2015 FIFA U-17 World Cup, South Korea advanced to the knockout stage as winner of their group by defeating Brazil and Guinea in the group stage. However, Lee missed a crucial penalty kick against Belgium in the round of 16 where they eventually lost 2–0. He shortly returned to South Korea afterwards to train with the second division side Suwon FC until January 2016, when he turned 18 and became able to participate in official matches for Barcelona again.

In May 2015, Lee was the youngest member of South Korea under-18 team that participated in the Suwon JS Cup, hosted by Park Ji-sung. In September 2015, he also played in an under-17 competition, Suwon Continental Cup, and scored two goals against Croatia. In March 2017, Lee participated in the Adidas U-20 Tournament to prepare the 2017 FIFA U-20 World Cup. He scored two goals against Zambia in the second game of the tournament, including a chip shot.

On 31 August 2017, Lee joined Italian club Hellas Verona on a four-year deal, for a fee of €1.5 million. Barcelona retains the option to repurchase him until 2019 for an undisclosed fee. On 24 September 2017, he made a Serie A debut for Verona in the second half of the game against SS Lazio. On 6 May 2018, he scored his first Serie A goal in an away match against Milan but his team lost 4–1. Verona was relegated to Serie B by finishing their league as 19th place. In the 2018–19 season, he recorded one goal and two assists in 27 appearances and his team was promoted to the Serie A by winning the promotion play-offs.

In May 2018, Lee was called for senior national side for the first time before 2018 FIFA World Cup, and was also named in South Korea’s preliminary 28-man squad. On 28 May 2018, he has played a big part in South Korea’s 2–0 victory over Honduras in Daegu Stadium. He showed short passes, bold dribbling and witty play in midfield, and also assisted Son Heung-min’s starting goal. He participated in two matches of the 2018 World Cup as a substitute.

On 30 August 2019, Lee joined Belgian First Division A side Sint-Truiden. He was excluded from the list in twelve consecutive matches and this caused much controversy in South Korea. On 29 November 2019, his name was on the list for the first time against Genk but didn’t appear. On 26 December 2019, he made his Belgian league debut against Waasland-Beveren. He finished his first season with only four appearances according to early termination of the Belgian league, caused by the COVID-19 pandemic.

On 13 September 2020, he scored his first and second goal for Sint-Truiden against Royal Antwerp, but his team lost 3–2 despite his two goals.