Lundkvist played as a youth within the Luleå HF organization of the Swedish Hockey League.

In his fourth season in the SHL in 2020–21, Lundkvist having evolved into a top pairing blueliner, recorded 14 goals and 18 assists for 32 points in 52 games for the team.

Following a postseason exit after seven playoff games, he was awarded the Salming Trophy as the league's best defenceman.

[3] On 3 June 2021, Lundkvist was signed by draft club, the New York Rangers, to a three-year, entry-level contract.

[5] Remaining on the Rangers roster to open the 2021–22 season, Lundkvist later scored his first NHL goal on 8 December 2021, at Madison Square Garden against the Colorado Avalanche.