The Dallas Stars saw enough potential in Lundkvist to acquire the right-shot defenseman in a trade with the New York Rangers on Sept. 19, 2022 for two conditional NHL Draft picks. Lundkvist was coming off a season when he had four points (one goal, three assists) in 25 games for the Rangers, and 15 points (three goals, 12 assists) in 34 games for Hartford of the American Hockey League, his first season in North America after New York chose him with the No. 28 pick in the 2018 NHL Draft.

Lundkvist signed a one-year, $1.25 million contract with the Stars on June 20, 2025, in lieu of becoming a restricted free agent. He was then given a two-year, $3.5 million contract (average annual value of $1.75 million) on April 17, 2026.

Lundkvist played four seasons for Lulea HF of the Swedish Hockey League, where he had 78 points (30 goals, 48 assists) in 166 career regular-season games. He was named the winner of the 2021 Salming Trophy, awarded annually to the best Swedish-born defenseman in the SHL, as selected by Hockey Hall of Famer Borje Salming. His 14 goals in 2020-21 were the most by a defenseman under the age of 21 in a single season in SHL history.

Lundkvist also represented Sweden at the 2018 IIHF U-18 World Championship, the 2019 and 2020 World Junior Championships and the 2021 World Championship. He won bronze at the tournaments in 2018 and 2020.