As a senior in 2015, he was the Los Angeles Times prep baseball player of the year after going 13–0 with a 0.34 earned run average (ERA).

[2][needs update] The Colorado Rockies selected Lambert in the second round of the 2015 Major League Baseball draft.

[7] He made his debut that same day at Wrigley Field versus the Chicago Cubs, giving up one run over seven innings while striking out nine, leading the Rockies to a 3-1 win.

On October 18, 2024, Lambert was removed from the 40–man roster and sent outright to Triple–A Albuquerque, but rejected the assignment and elected free agency.

[11] On December 14, 2024, Lambert signed a one–year, $1.6 million contract with the Tokyo Yakult Swallows of Nippon Professional Baseball.