In 2016, Lawrence played in 12 games for the Tigers at defensive tackle. Throughout the regular season, he recorded 55 tackles and 5 sacks. The 5 sacks he recorded in his freshman year is a Clemson record. Lawrence beat the previous record of 4 set by William Perry, Ricky Sapp, and Shaq Lawson. Lawrence was subsequently named the 2016 ACC Defensive Rookie of the Year.[7] Lawrence was part of the Clemson team that defeated Alabama in the 2017 College Football Playoff National Championship by a score of 35–31. In the game, he recorded four total tackles.[8] Dexter was ruled ineligible for the 2019 College Football Playoff after testing positive for the banned substance ostarine.[9][10] After the season, Lawrence decided to forgo his senior year and enter the 2019 NFL draft.[11]
In Week 1 of the 2020 season against the Pittsburgh Steelers on Monday Night Football, Lawrence recorded his first sack of the season on Ben Roethlisberger during the 26–16 loss.[19]
During Week 2 of the 2021 season against the Washington Football Team, Lawrence jumped offsides on the final play of the 4th quarter, a Dustin Hopkins missed field goal, which nullified the Washington kick attempt. The Giants would lose 29–30 on Hopkins' successful re-kick, dropping to 0–2 for the fifth consecutive season.[20]
On April 28, 2022, the Giants picked up the fifth-year option on Lawrence’s rookie contract.[21]
2022 was a career year for Lawrence. In Week 4, he tallied 2 sacks against the Chicago Bears, the first multi-sack game of his career, then earned praise from Aaron Rodgers following their comeback victory over the Green Bay Packers a week later.[22] In a Week 15 tilt against the Washington Commanders, he forced an incomplete pass from Taylor Heinicke that turned out to be a key forced fumble which the Giants recovered. The Giants made the playoffs in 2022 for the first time in his career. He finished the 2022 season with 7.5 sacks, 68 tackles, 28 quarterback hits and 2 forced fumbles. As well as being selected to his first Pro Bowl and first All-Pro team.
On May 4, 2023, Lawrence signed a four-year extension with the Giants.[23]
In Week 8 of the 2023 New York Giants season, Lawrence had a recorded a sack, a tackle-for-loss, 5 quarterback hits, and 15 quarterback pressures against the New York Jets, which tied the record for the most pressures in a single game by an interior defender.[24]