Lammers grew up near the Zandvoort circuit, encouraged by Dutch touring-car legend Rob Slotemaker, who recognised his talent while Lammers was still too young for a standard driving licence. Competing in a Simca Rallye 2 in the 1973 Dutch Touring Car Championship, Lammers won his first car race and took the season title at just sixteen years old, becoming the youngest Dutch national champion in history. He repeated the feat in 1976 in an Opel Kadett.
Moving into single-seaters, Lammers claimed the 1978 European Formula 3 Championship with Racing Team Holland, beating future world champions Alain Prost, Nelson Piquet, and Nigel Mansell in the process. He remains the only Dutch driver to have won that title. British magazine Autosport predicted at the time that he "just has to be a World Champion of the eighties."
Lammers made his Formula One debut with Shadow in 1979 alongside rookie Elio de Angelis, but the team was close to collapse. Over four seasons he drove for Shadow, ATS, Ensign, and Theodore, making 23 championship starts without scoring a World Championship point. The machinery was almost uniformly uncompetitive, though his talent was widely recognised. At ATS he immediately qualified fourth on the grid at Long Beach before mechanical failure ended his race on the opening lap.
Among the near-misses that defined his Formula One tenure: in 1982 he was approached by Ferrari to replace the late Gilles Villeneuve, but a thumb injury sustained when his Theodore's throttle stuck at Detroit prevented him from signing the contract. Patrick Tambay got the drive instead. He was also tested by Ken Tyrrell in 1989 as a replacement for Michele Alboreto but chose to remain with TWR Jaguar; Tyrrell signed Jean Alesi instead.
In 1992, Lammers made a surprise return to Formula One with March for the final two races of the season — a ten-year gap that stood as a record in the sport. He retired from the Japanese Grand Prix with a broken gearbox and finished twelfth at Adelaide before the team folded in early 1993.
Lammers' pivot to sportscars from 1983 onwards proved the making of his career. He joined top Porsche privateer Richard Lloyd Racing for the World Sportscar Championship, taking several podium finishes before being recruited mid-1984 by Tom Walkinshaw for TWR Jaguar.
After developing his Group C skills through 1985 and 1986, Lammers became a full TWR Jaguar works driver for the 1987 season, sharing with John Watson and winning at Jarama, Monza, and Fuji. The 1988 campaign brought his defining moment: paired with Johnny Dumfries and Andy Wallace at Le Mans, Lammers drove thirteen hours of the twenty-four and anchored the team to victory. Following the win he was congratulated by Queen Elizabeth II and made an honorary member of the British Racing Drivers' Club.
He also won the Daytona 24 Hours with Jaguar in 1988 and 1990. After a move to Toyota in 1992, Lammers won the Japanese Sports-Prototype Championship with two victories at Fuji and Mine.
In 2001, Lammers created the Racing for Holland team, entering the new FIA Sportscar Championship with a Dome S101 chassis. Running the car with a distinctive chequered-sponsor livery — small companies could buy space on the bodywork for 2,200 euros — the team and Lammers took three wins and five podiums en route to the 2002 championship in the SR1 class. He successfully defended the title in 2003 with an identical haul of results.
Racing for Holland continued at Le Mans until 2007, by which point the Dome design had been overtaken by newer prototypes. Lammers' final Le Mans appearances came in 2017, 2018, and 2019 with Racing Team Nederland in LMP2, sharing at various points with Rubens Barrichello and team owner Frits van Eerd.
Outside of his own driving, Lammers ran the Vitaal Racing Formula Opel Lotus team from 1989 to 1991, winning the EFDA Opel Lotus Euroseries with Peter Kox in 1989. He held the A1 Grand Prix Netherlands seat from 2005 to 2009, fielding Jos Verstappen and Jeroen Bleekemolen among others.
After retiring from active competition following the 2019 Le Mans, Lammers became sporting director of the organisation that revived the Dutch Formula One Grand Prix at Zandvoort, an event that returned to the calendar in 2021 for the first time since 1985.
Lammers demonstrated remarkable breadth throughout his career. He won the European Renault 5 Turbo Cup in 1983 and 1984. He competed in IndyCar in 1985 and 1986 with Dan Gurney's All American Racers. He twice finished third in the Macau Grand Prix Formula Three support race during the mid-1980s. He raced in the British Touring Car Championship in 1994 for TWR's Volvo team alongside Rickard Rydell, and contested five Dakar Rallies between 2010 and 2014. He also participated in Formula 3000 at various points in his career.
Lammers is one of the most versatile professional racing drivers in modern motor sport history, with serious competitive results across touring cars, Formula Three, Formula One, IndyCar, Group C prototypes, GT racing, rallycross, and rally-raid over more than forty years. His 1988 Le Mans victory with Jaguar stands as his most celebrated achievement, recognised at the highest level by the British Crown. His role in bringing Formula One back to Zandvoort represents a second significant contribution to the sport beyond his driving career.