Born in the French overseas department of Martinique and raised in Le Morne-Vert until the age of 15,[1] Lessort joined the youth ranks of Élan Chalon in 2010 and won the French national championship with Chalon’s cadet team in 2012 and 2013 and with their development team ("Espoirs") in 2013.

[2] Lessort was handed his first professional contract by the club in June 2014[3] and made his debut in the French top-flight Pro A during the 2014–15 season.

[14] On 25 September 2021, Lessort signed a 2-month contract with Maccabi Tel Aviv of the Israeli Premier League in order to replace the injured Ante Žižić.

Partizan ended the 2022–23 season by lifting the ABA League championship trophy, after 3–2 score against Crvena zvezda in the Finals series.

On February 29, 2024, in a 97–86 win against Real Madrid, Lessort set his EuroLeague career-high of 26 points, alongside 7 rebounds and 4 assists.

On December 19, Lessort sustained an injury when he fractured two bones in his right lower leg leaving him out for a significant amount of the season.

[20] On December 31, 2024, Lessort officially signed a three-year contract extension with the defending EuroLeague champions through 2028.

[25] Lessort played in the 2013 Nike Global Challenge, averaging 19.5 points, 7.8 rebounds and 1.3 blocks a game,[26] while receiving International All-Tournament Team honors.