[2] He rode in 2013 for King's Lynn Young Stars in the National League, scoring 15 points in his first meeting and winning five of his six races, and was promoted straight into main body of the Stars Elite League team the following year, with the team's early fixtures arranged to ensure that he reached the age of 16 before the first meeting.

[11] In 2020, Lambert became the first British rider to win the Speedway European Championship when the competition was held exclusively in Poland (over 5 rounds) due to the COVID-19 pandemic.

[14] Towards the end of the 2022 season Lambert returned to ride in the United Kingdom for Belle Vue Aces in the play offs, as a replacement for the injured Max Fricke.

Lambert was the leading rider on the night but just failed to hold off Maciej Janowski in the last heat, which would have forced a run-off.

[20] Lambert starred again as he helped Great Britain secure the 2024 Speedway of Nations in Manchester, which was his second world team title,[21] and then won his maiden Grand Prix in Vojens.