Johansen was originally drafted by the Kelowna Rockets, 119th overall in the 2012 WHL Bantam draft, and played two seasons of midget hockey in the BC Hockey Major Midget League with the Vancouver North East Chiefs before joining the Rockets for the 2014–15 season.

On March 2, 2017, Johansen was signed to a three-year, entry-level contract with the Washington Capitals.

[1] At the conclusion of his third season with the Rockets in 2016–17, Johansen signed an amateur try-out contract to join the Capitals' American Hockey League affiliate, the Hershey Bears, during their post-season run on May 2, 2017.

Johansen was cut from the 2017–18 Washington Capitals training camp, and reassigned to Hershey for the 2017–18 AHL season.

[4] Lucas' older brother Ryan is a forward who currently plays for the Lehigh Valley Phantoms while under contract to the Philadelphia Flyers.