[5] Entering the 2021–22 season, Lambert was considered one of the top prospects for the upcoming 2022 NHL entry draft, ranked as high as second overall by some scouts.

[6] After a disastrous start to the season that saw him score only six points in 24 games, Lambert's contract was terminated by mutual agreement and he signed with his hometown club, the Lahti Pelicans.

[10] On 12 October 2022, he was signed to a three-year entry-level contract and assigned to the Jets' American Hockey League (AHL) affiliate, the Manitoba Moose.

[15] With multiple Jets regulars not playing the final game of the season to rest ahead of the playoffs, Lambert was recalled to the NHL.

[17] Lambert represented Finland at the 2019 Hlinka Gretzky Cup, as a 15-year-old at the under-18 tournament, where he scored a hat-trick in a 6–0 victory against Switzerland.