Lemieux played minor ice hockey with the Lemieux Academy in Phoenix, and participated in the 2008 and 2009 Quebec International Pee-Wee Hockey Tournaments with the team.
Junior
Lemieux joined the Barrie Colts of the Ontario Hockey League part-way into the 2012–13 OHL season after starting the season in the United States Hockey League with the Green Bay Gamblers. He was named to play with the gold medal winning Canadian squad at the 2013 Ivan Hlinka Memorial Tournament, and was also selected to skate in the 2014 CHL/NHL Top Prospects Game. During the 2014 NHL Entry Draft, Lemieux was selected in the second round, 31st overall by the Buffalo Sabres. Lemieux was assigned to the Colts for the subsequent season. On February 11, 2015, Lemieux was traded to the Winnipeg Jets as part of a blockbuster deal that saw him, Tyler Myers, Joel Armia, Drew Stafford, and a 2015 conditional first round pick go to Winnipeg in exchange for Evander Kane, Zach Bogosian, and the rights to Jason Kasdorf. It was later revealed that Lemieux had requested a trade from the Sabres and on July 3, 2015, he was signed to a three-year entry-level contract by the Jets. On December 10, 2015, during his final eligible junior season in 2015–16, Lemieux, alongside a 2017 third-round and a 2020 fourth-round pick was traded to the Windsor Spitfires in exchange for Anthony Stefano, a 2019 third-round and 2021 second-round pick. He finished the season with 34 goals and 62 points.
Professional
Lemieux made the transition to professional hockey during the 2015–16 season, appearing in five games for the Jets' American Hockey League affiliate, the Manitoba Moose. Lemieux recorded two goals and one assist. In his first full professional season, Lemieux skated in 61 games for the Moose, recording 12 goals and seven assists for 19 points. The following season, after recording three goals and two assists in four games with the Moose, Lemieux received his first call-up by the Jets, and made his NHL debut on October 20, 2017. He went scoreless in 9:53 on-ice time in a 4–3 win over the Minnesota Wild. Lemieux's first career NHL goal came on October 29 in a 7–1 win over the Pittsburgh Penguins, redirecting a Tyler Myers point shot. In the following 2018–19 campaign, Lemieux made the Jets opening season roster for the first time, securing a role on Winnipeg's fourth-line. On November 2, 2018, Lemieux delivered an illegal check to the head of Florida Panthers' forwardVincent Trocheck. He was given a match penalty for the incident. Three days later, Lemieux received a two-game suspension. Having already established career highs through 44 games with the Jets, Lemieux was dealt at the trade deadline, along with a 2019 first-round pick and a conditional fourth round pick, to the New York Rangers in exchange for Kevin Hayes on February 25, 2019. On March 1, 2019 Lemieux scored his first goal as a Ranger in a 4–2 home loss against the visitingMontreal Canadiens. On March 13, 2020, it was announced that Lemieux would be suspended for his hit on Joonas Donskoi, but that the precise parameters of the suspension would be determined and announced once resumption of play guidelines have been established. As the league began their return to play protocols, it was announced that Lemieux would be suspended for two Stanley Cup Qualifying games.
Playing style
Player agent Tyler Parchem described Lemieux as:
Personal life
Lemieux is the son of the former NHL right winger Claude Lemieux. Lemieux was born in Denver during his father's tenure with the Colorado Avalanche and as a result of his career, he grew up in Denver, New Jersey, Phoenix and Dallas. Lemieux has a younger sister and two paternal half-brothers from his father's first marriage.