Born in Hastings but raised in Pukekohe, Lawson began karting at the age of seven, competing in numerous championships across New Zealand, including two karting titles in 2014.
Lower formulae
In 2015, Lawson made his single-seater debut in the Formula First Manfield Winter Series with Sabre Motorsport, taking a win and ten podiums to finish second overall. A few months later, he joined Sabre to contest the NZ Formula First championship, taking a win and three podiums on his way to sixth in the championship and the Rookie of the Year title. The following year, Lawson graduated to the NZ F1600 Championship Series. There he dominated proceedings, claiming fourteen of the fifteen victories on offer to become the youngest champion in not just the series' history, but the youngest ever Formula Ford champion in world at the time. In 2017, Lawson moved up to the Australian F4 championship with BRM, taking five wins to finish as vice-champion in only his rookie season. The following year, Lawson remained at Formula 4 level, moving across to contest the ADAC Formula 4 championship with Van Amersfoort Racing and received backing from Turner's, the New Zealand used car network that had previously sponsored IndyCar champion Scott Dixon. Claiming three wins and three pole positions, Lawson's performances saw him claim his second consecutive F4 vice-champion position.
In November 2018, Lawson joined M2 Competition for the 2019 championship. Lawson dominated on debut at Highlands, taking 2 races wins by over nine-seconds each and won the Dorothy Smith Memorial Trophy as a result of winning Race 3. Claiming three additional wins across the season, Lawson secured the title at the New Zealand Grand Prix after a season long battle with Ferrari junior and fellow countryman Marcus Armstrong.
Lawson had been set to join the inaugural season of the Formula European Masters with Motopark, alongside fellow Red Bull Junior Yuki Tsunoda, but followed the German outfit to the Euroformula Open Championship when Formula European Masters was cancelled due to a lack of entrants.
In November 2018, Lawson competed in the season finale of the Asian F3 championship with Irish outfit Pinnacle Motorsport. He proceeded to dominate the weekend, taking all wins, fastest laps and pole positions on offer to finish eighth in the championship.
In December 2017, Lawson partook in the Mazda Road to Indy Shootout, finishing as the fastest driver but losing out on the scholarship to Ireland's Keith Donegan.