Born in Zandvoort, Lammers grew up around motorsport through Dutch touring-car legend Rob Slotemaker's skid-school. Driving a Simca Rallye 2 in 1973, he won the Dutch Touring Car Championship at 16, becoming the youngest Dutch national auto racing champion in history. He won a second Dutch touring-car title in 1976 in an Opel Kadett GT/E.
Lammers moved into Formula Ford in 1976 alongside his touring-car campaign. Stepping up to Formula 3 in 1978 with the Racing Team Holland outfit run by Alan Docking, and with future Formula One drivers Huub Rothengatter and Arie Luyendijk as teammates, he won the 1978 European Formula 3 Championship. He beat Anders Olofsson to the title while defeating highly regarded contemporaries including Alain Prost, Nelson Piquet, and Nigel Mansell. He remains the only Dutch driver to have won the European F3 title.
Lammers spent four seasons in Formula One between 1979 and 1982, making 41 World Championship starts across the Shadow, ATS, Ensign, and Theodore teams without scoring a point. He was widely regarded as talented but hampered by consistently uncompetitive machinery.
At Shadow in 1979 he was partnered with Elio de Angelis; both drivers invited by Colin Chapman to test for Lotus, de Angelis secured the drive while Lammers declined to wait for a decision. Moving to ATS in 1980, he qualified fourth at Long Beach on his first outing with the new D4 car, only for it to fail on the opening lap. At Theodore in 1982 he came close to replacing Gilles Villeneuve at Ferrari after Villeneuve's death at Zolder, but a throttle-stick incident in practice at Detroit caused Lammers to break his thumb, and Patrick Tambay signed the Ferrari contract in his place.
Lammers made a surprise Formula One comeback in 1992 with March, replacing Karl Wendlinger for the final two races of the season — a gap of ten years between his first and second spells, a record career break in the championship. He retired from the Japanese Grand Prix with a broken gearbox and finished twelfth in Australia. Plans for 1993 collapsed when March lost their engine deal.
After stepping back from Formula One, Lammers built an extensive sportscar career centred on the World Sportscar Championship and the Le Mans 24 Hours. He joined privateer Porsche team Richard Lloyd Racing in 1983, taking several podium finishes before a mid-season switch to TWR Jaguar in 1984.
The defining moment of his career came in 1988. Partnered with Johnny Dumfries and joined at Le Mans by Andy Wallace, Lammers drove for 13 hours to anchor a winning effort for TWR Jaguar. It was Jaguar's first Le Mans victory since 1957. Queen Elizabeth II congratulated Lammers personally and he was named an Honorary Member of the British Racing Drivers' Club. He also won the 1988 Daytona 24 Hours, having been moved from a retired car to join Martin Brundle, Raul Boesel, and John Nielsen in the lead Jaguar entry. In 1990, Lammers won the Daytona 24 Hours again with Andy Wallace and Davy Jones.
After a brief spell with the Toyota works sportscar programme, during which he won the 1992 Japanese Sports-Prototype Championship, Lammers established his own team Racing for Holland in 2001. Running the Japanese Dome S101, the team won the FIA Sportscar Championship in both 2002 and 2003.
Lammers had three distinct spells as a team principal. Between 1989 and 1991 his Vitaal Racing outfit competed in Formula Opel Lotus, winning the EFDA Opel Lotus Euroseries with Peter Kox in 1989. Racing for Holland, founded in 2001, won back-to-back FIA Sportscar titles before the championship collapsed after 2003. Between 2005 and 2009 Lammers managed the Dutch A1 Grand Prix team, with Jos Verstappen as his first driver.
Lammers continued racing at Le Mans until 2018, his final competitive appearances coming with Racing Team Nederland in the LMP2 class. After retiring in 2019, he became sporting director of the organisation that revived the Dutch Grand Prix at Zandvoort. The first Dutch GP since 1985 was staged in 2021, with Lammers a central figure in bringing it about.
His career also included European Renault 5 Turbo Cup titles in 1983 and 1984, an IndyCar stint with Dan Gurney's All-American Racers in 1986, a third-place finish at the Macau Grand Prix in 1985, a season in the British Touring Car Championship with Volvo, GT appearances spanning BPR, FIA GT, and ADAC GT, and five starts at the Dakar Rally. Lammers is widely recognised as among the most versatile drivers of the modern era across circuit racing disciplines.