Lapierre began karting in 1993 and progressed through French Formula Renault before moving to the Formula Three Euroseries with Signature in 2003. Despite modest points finishes in the Euroseries that year, he won the prestigious Macau Grand Prix on the streets of the former Portuguese territory. He stayed in Formula Three in 2004, winning at Pau and twice at the Hockenheimring to finish third in the standings.
He progressed to the GP2 Series in 2005 with Arden International, scoring the first pole position in GP2 history but ending the year twelfth in the standings. Between 2005 and 2007, Lapierre also competed in the A1 Grand Prix series for A1 Team France, helping the team win the series championship through multiple sprint and feature race victories. He continued in GP2 through 2007, claiming victories at Bahrain and Spa-Francorchamps before concluding his single-seater career.
Lapierre transitioned to sportscar racing full-time in 2008 with Team Oreca-Matmut in the Le Mans Series LMP1 category alongside former Formula One driver Olivier Panis. After several seasons in LMP1, he became a Toyota factory driver in 2012 for the newly-formed FIA World Endurance Championship, sharing the No. 7 Toyota TS030 Hybrid with Alexander Wurz. The pair contributed to Toyota taking wins at São Paulo, Fuji, and Shanghai in their debut WEC season. Lapierre remained at Toyota through 2014, recording a third-place overall finish at Le Mans that year before losing his seat following two wet-weather accidents.
Stepping down to LMP2 in 2015, Lapierre drove for KCMG at Le Mans and took a class victory despite a late off-track excursion that required marshal assistance. He joined Signatech Alpine in the WEC for 2016, where he partnered Gustavo Menezes and Stéphane Richelmi to win the LMP2 championship with seven podiums including a class victory at Le Mans. Over the following seasons with Alpine, Lapierre built one of the most consistent LMP2 records in the WEC era.
In the 2018–19 WEC "Super Season," Lapierre shared the Alpine entry with André Negrão and Pierre Thiriet, finishing on the podium in every race of the season and winning the LMP2 title. The crew won the Le Mans class twice across the super season's two Le Mans races — in 2018 after a rival's disqualification, and in 2019 outright — making Lapierre a four-time class winner at Le Mans in four entries.
Lapierre entered the Hypercar class with Alpine in 2021, driving the grandfathered Alpine A480 alongside Matthieu Vaxivière and André Negrão. The trio finished on the podium in every race of the season. He returned to the Hypercar class in 2024 in the new Alpine A424 alongside Vaxivière and Mick Schumacher, before announcing his retirement on 2 October 2024. His final race was the 2024 6 Hours of Fuji, where he finished third.
Lapierre is one of the most successful LMP2 drivers in Le Mans history, with four class victories at the circuit across four appearances. His partnership with Toyota in the WEC's early years helped establish the Japanese manufacturer's endurance racing programme. After retirement from driving, he became team principal of COOL Racing — a team he had co-invested in — and was named Sporting Director for Alpine's endurance programme in 2025. He is also a two-time winner of the 12 Hours of Sebring and the 2003 Macau Grand Prix champion.