[3][4][5] Birutis made a strong debut on 15 April 2017, scoring 17 points and grabbing four rebounds, but his team lost 92–89 after Justas Tamulis buzzer-beater.

[8] During the 2018 Karaliaus Mindaugo taurė quarterfinals against the Lithuanian champions Žalgiris Kaunas, Birutis played the best game of his career by scoring 35 points, grabbing 11 rebounds, dishing out 2 assists and blocking one shot, although his team lost 85–78.

Birutis joined Lithuanian champions Žalgiris Kaunas and made his EuroLeague debut on 12 October 2018 against Saski Baskonia.

Birutis struggled with injury since the start of the season and was unable to train due to pain, which led to surgery on 14 February 2019.

On November 23, he made his return to the court, scoring nine points and four rebounds in 16 minutes, including the game-winning shot, in a thrilling 81–79 win over BC Pieno žvaigždės.

[18] Laurynas Birutis debuted for the Lithuania men's u-16 basketball team at the 2013 FIBA Europe Under-16 Championship in Ukraine.

Birutis, along with his teammates and generational peers Tadas Sedekerskis and Martynas Varnas, was invited to play at the FIBA's Youth All-Star Game during EuroBasket 2015.