Lundgaard started karting in 2012, competing all across Europe and collecting three major titles in the 2012 Denmark Cadett Junior Kart Cup South, 2015 CIK-FIA European KF-Junior Championship and the 2015 KFJ South Garda Winter Cup. In 2017 he made the step up to SMP F4 and Spanish F4 with Dutch team MP Motorsport, claiming 9 victories in SMP F4 and clinching the title with one round to go. He also went on the win the Spanish F4 Championship. Alongside this, Lundgaard also competed in the F4 Danish Championship where he placed 11th. He was added to the Renault Sport Academy in relation to the Renault F1 Team. In 2018, Lundgaard remained with MP Motorsport but moved to the Formula Renault Eurocup and NEC championships. He claimed 4 wins across the season in Eurocup and ended up vice-champion and rookie champion at the end of the season. He took a further 2 wins in the NEC and placed 11th. Christian also debuted in the GP3 series with the team for two races, finishing 23rd.
In 2019, Lundgaard signed with ART Grand Prix for the FIA F3 season, losing his first victory due to a 5 second penalty for a virtual safety car infringement. He eventually claimed his first victory at the Hungaroring. He finished the season in sixth place, returning in November to Macau with ART Grand Prix. He claimed a third place in the qualification race and fourth in the main race. Alongside this, Lundgaard competed with Pinnacle Motorsport in the F3 Asian Winter Series as a guest.
FIA Formula 2
In 2019, Lundgaard teamed up with Trident for the final round of the FIA Formula 2 season, not scoring any points but gaining valuable experience.
In January 2020, it was announced Lundgaard would remain in F2 but with his previous team, ART Grand Prix, teaming up with Marcus Armstrong.