[3] Luukkonen grew up idolizing Finnish goaltenders Miikka Kiprusoff and Tuukka Rask.

[10] In the 2018–19 season, his first in North America playing major junior ice hockey, Luukkonen set the Sudbury Wolves franchise record for most wins in a regular season,[11] and led the Ontario Hockey League (OHL) in wins, save percentage, and shutouts.

[16] On 14 April, Luukkonen made his debut with Rochester, earning a victory in a 4–2 win over the Belleville Senators.

[20] On 18 August 2020, Luukkonen agreed to return to the Finnish Liiga on loan from the Sabres with TPS for a period of four-to-six weeks due to the delayed 2020–21 North American season.

[25] Luukkonen began the 2022–23 season with the Americans to ensure he could get ice time,[26] before being called up due to an injury to Eric Comrie.

During a road trip in December 2023, Luukkonen had "two stellar showings out west...he was decisive and showed off his athletic ability", including a 41-save performance against the Vegas Golden Knights where Tage Thompson said Luukkonen "won the game for us.

[30] During the off-season in the spring of 2023, Sabres general manager Kevyn Adams invited Luukkonen to his house to have dinner and watch the Stanley Cup playoffs.

[6] Luukkonen's first start of the season came on the second half of a back-to-back series on 24 October 2023, a 6–4 win against the Ottawa Senators.

His next ice time would come in relief in the next game after Comrie was injured against the New Jersey Devils.

However, Luukkonen entered the new year on a hot streak, including two consecutive shutouts on 15 and 18 January 2024, against the San Jose Sharks and Chicago Blackhawks,[37][38] becoming the first Sabres goaltender to accomplish that feat since Carter Hutton in 2019.

[40][41] He led the league in save percentage and goals against average from 1 January until 15 February, where he missed a game due to a lower-body injury.

[45][46] Luukkonen was nominated by the Professional Hockey Writers' Association (PHWA) for the 2024 Bill Masterton Memorial Trophy.

[50] After the season, Luukkonen filed for salary arbitration, however prior to the hearing, he and the Sabres agreed to terms on a five-year, $23.75 million contract extension, including a five-team no trade clause after two years.