As a youth, Lashoff played in the 2003 Quebec International Pee-Wee Hockey Tournament with the New York Rangersminor ice hockey team. Undrafted, Lashoff played major junior hockey in the Ontario Hockey League with the Barrie Colts and Kingston Frontenacs. On October 1, 2008 he was signed to an entry-level contract with the Detroit Red Wings organization following their 2008 training camp. At the beginning of the lockout shortened 2012–13 season, Lashoff was recalled by the Red Wings after an injury to Jonathan Ericsson on January 21, 2013. He made his NHL debut the same day against the Columbus Blue Jackets, and scored his first goal in the second period against Sergei Bobrovsky. On May 11, 2013, after being sent down from Detroit, Lashoff returned to the Grand Rapids Griffins to help them during their 2013 Calder Cup run. During the 2012–13 season, Lashoff recorded two goals and four assists in 37 regular season games, and one assist in 18 postseason games. On January 30, 2015, Lashoff was placed on waivers by the Red Wings. After clearing waivers, Lashoff was assigned to the Grand Rapids Griffins. Prior to being placed on waivers, Lashoff appeared in 11 games for the Red Wings during the 2014–15 season, where he recorded two assists. On June 16, 2016, the Red Wings signed Lashoff to a one-year contract extension. During the 2016–17 season, Lashoff recorded three goals and eights assists in 62 games during the regular season. During the 2017 Calder Cup playoffs, he recorded one goal and three assists in 17 playoffs games, and helped lead the Griffins to the Calder Cup. On June 29, 2017, the Red Wings signed Lashoff to a two-year contract extension. On December 6, 2018, Lashoff was recalled by the Red Wings. Prior to being recalled, he recorded three assists in 17 games for the Griffins. On March 13, 2019, the Red Wings signed Lashoff to a two-year contract extension. On December 27, 2019, the Red Wings recalled Lashoff from the Griffins. Prior to being recalled, he recorded two goals and 12 assists in 25 games for the Griffins.
Brian's older brother, Matt, has also played professionally in the NHL and currently plays for the SCL Tigers of the National League A. Their first game played against each other in an organized league was December 22, 2010 when the Grand Rapids Griffins met the Toronto Marlies in an AHL game.