Lapierre began karting in 1993, finishing third in the French championship in 1996 and reaching the finals of the European Junior Championship in 1998. He competed in French Formula Renault from 1999 to 2002, adding some Formula Renault 2.0 Eurocup appearances and limited French Formula Three outings.
In 2003, Lapierre moved to the Formula Three Euro Series with Signature. His season yielded only a single podium, leaving him eleventh overall — but he made his mark at Macau, winning the prestigious Macau Grand Prix. He returned to the Euroseries in 2004, winning at Pau and twice at the Hockenheimring en route to third in the standings.
Lapierre entered the newly restructured GP2 Series in 2005 with Arden International, partnering Heikki Kovalainen. He secured the first pole position in the championship's history but was unable to start the race, and the season ended disappointingly with twelfth place. Alongside GP2, he drove for A1 Team France in the A1 Grand Prix series — winning both sprint and feature races in Germany and Australia, the main race in Dubai, and the sprint in Indonesia, contributing significantly to France's championship title.
He remained with Arden in GP2 for 2006, taking three podiums in the opening three rounds, before a crash at Monaco caused two compressed vertebrae and forced him to miss two rounds. He returned to finish ninth. In 2007, driving for DAMS in GP2, Lapierre won the Bahrain sprint race and claimed a feature race victory from pole at Spa-Francorchamps, ending the year twelfth overall.
Lapierre transitioned to sportscars full-time in 2008, joining Team Oreca-Matmut in the LMP1 category of the Le Mans Series alongside former Formula One driver Olivier Panis. The partnership continued through 2010, including a season where Lapierre finished second in the Le Mans Series drivers' championship, winning from pole at the Algarve in a Peugeot 908 HDi FAP.
In 2011, Lapierre, Panis, and Loïc Duval won the opening round of the Intercontinental Le Mans Cup at Sebring, beating the Peugeot works entry.
Lapierre became a Toyota factory driver in 2012 for the inaugural FIA World Endurance Championship season, sharing the No. 7 Toyota TS030 Hybrid with Alexander Wurz. After retiring at Le Mans — having briefly led late on Saturday evening before an engine failure — the pair won at São Paulo, Fuji, and Shanghai to finish third in the championship.
In 2013, Lapierre, Wurz, and Kazuki Nakajima faced a difficult first half before reviving with a rain-shortened victory in Japan and a second place from pole in China. The 2014 season saw Lapierre partner Anthony Davidson and Sébastien Buemi, winning twice with the No. 8 entry at Silverstone and Spa, and recording his best Le Mans result to that point with third overall. However, Toyota dropped him after Austin, citing personal reasons — though two accidents in wet conditions at Le Mans and Austin were widely reported as contributing factors.
From 2015 onwards Lapierre competed primarily in LMP2. He won the class at Le Mans in 2015 with KCMG, despite a late off-track excursion requiring marshal assistance. In 2016, driving for Signatech Alpine in the WEC alongside Gustavo Menezes and Stéphane Richelmi, the team secured the LMP2 championship with seven podiums including a class win at Le Mans.
The 2018–19 WEC Super Season represented the peak of Lapierre's LMP2 achievement. Partnering André Negrão and Pierre Thiriet for Alpine, the trio finished on the podium in all eight rounds to take the LMP2 championship. Their two class victories were both at Le Mans: in 2018 inherited via a G-Drive Racing disqualification, and in 2019 earned outright — making Lapierre a four-time Le Mans LMP2 winner.
Lapierre joined Alpine's WEC Hypercar lineup in 2021, driving the grandfathered Alpine A480 alongside Matthieu Vaxivière and André Negrão. With Toyota dominating as the only other full-time competitor, Alpine finished all six rounds on the podium and took third in the championship. After further seasons in LMP2 with Cool Racing in the ELMS while maintaining Alpine hypercar commitments, Lapierre returned to Alpine's WEC Hypercar entry in 2024, driving the A424 alongside Vaxivière and Mick Schumacher.
He announced his retirement on 2 October 2024 ahead of the Bahrain finale. His final race, the 6 Hours of Fuji, ended with a third-place podium. Days after his retirement announcement, Lapierre was named Sporting Director for Alpine's endurance programme.
He also became team principal of Cool Racing — renamed Cool Racing / CLX Motorsport with the L representing Lapierre — from the end of 2020.
Lapierre's career arc — from Macau Grand Prix winner and GP2 front-runner to Toyota factory pilot and four-time Le Mans LMP2 class winner — reflects a versatile career that found its true expression in endurance racing. His four Le Mans class victories, two Sebring wins, and WEC championship with Alpine anchor a record that places him among the most decorated French endurance drivers of his generation.