Lawrence Clark grew up in Camden, New Jersey, across the river from Philadelphia, in a family with no musical background. He started on alto and baritone saxophone in his middle and high school concert and jazz bands, and during his senior year won a scholarship for private lessons at the Settlement Music School in Philadelphia. A partial scholarship then took him to Berklee College of Music in Boston, where he shifted his focus to tenor saxophone, the horn he has played ever since, studying under Fred Lipsius, Andy McGhee, and Billy Pierce.

After several years in Boston, Clark relocated to New York City, where he began what became a decade-long apprenticeship in drummer Rashied Ali's working band, roughly from 2000 until Ali's death in August 2009. "Rashied was not only my mentor but also my good friend, like family," Clark has said of the relationship. The best-documented product of that apprenticeship is a session recorded February 17-18, 2005, at Ali's own Survival Studio in New York, with bassist Joris Teepe, pianist Greg Murphy, and trumpeter Jumaane Smith, released the following year on Survival Records as the double album Judgment Day, Vol. 1 and Vol. 2. AllMusic's Michael Nastos called Volume 1 "a rock-solid recording from beginning to end," writing that "all of those interested in modern mainstream jazz should pay close attention to it," while JazzTimes' Chris Kelsey described the music as swinging "in a way guaranteed to make the Lincoln Center cats swallow hard and take notice." The same working quintet, with trumpeter Josh Evans in Smith's chair, reconvened on November 2, 2007, for a performance at the Jazz Happening festival in Tampere, Finland, issued posthumously in 2009 as Live In Europe (Survival Records SR 126), its four tracks drawn mostly from the book of guitarist James "Blood" Ulmer, a former Ali bandmate, plus one Clark original.

Alongside the Ali association, Clark built a busy career as a New York sideman through the 2000s. He appears on drummer Winard Harper's Make It Happen (2006, Piadrum Records), a sextet date with alto saxophonist Antonio Hart, trombonist Wycliffe Gordon, fellow tenor player Stacy Dillard, and trumpeter Josh Evans; on pianist Greg Murphy's own leader debut, Orientation (2006, Murphasaurus Records), alongside percussionist Raphael Cruz; and on two early-2000s releases by the Philadelphia jazz-funk duo Supa Lowery Bros., Vol. 1 (2004) and Vol. 2 (2006). In the 2010s he turned up repeatedly on trumpeter Josh Evans's leader dates, including Portrait (2011, Snavesounds), with drummer Ralph Peterson and bassist Dezron Douglas, which carries one composition co-credited to Rashied Ali, and Hope And Despair (2015, Passin' Thru Records), with saxophonists Abraham Burton and Bruce Williams, pianist David Bryant, and cover photography by Oliver Lake. He also became a regular in drummer George Spanos's downtown, nu-jazz-adjacent circle, recording on Dreams Beyond (2014), Reflections (2017), and the two-volume Upside Down (2019), sessions that also drew players like Daniel Carter and Juini Booth from New York's avant-garde scene.

Clark issued his own recording debut, Forward Motion, as a self-released digital album on July 1, 2017, an eight-track quintet date with trumpeter Josh Evans, pianist David Bryant on Rhodes, bassist Rahsaan Carter, and drummer Kush Abadey. His sophomore album, Inner Visions, followed on August 9, 2019, on the European label Jazz Tribes, recorded September 17, 2018, at Tedesco Studios in Paramus, New Jersey, with trumpeters Jeremy Pelt and Duane Eubanks, pianist David Bryant on piano and Rhodes, bassist Joris Teepe, and drummer Darrell Green. The nine-track record opens and closes with "Mr. Ali" and "Mr. Ali 2," a pair of loose, free-time trio tributes to his late mentor, and includes "Blew" and "Freedom," two pieces Clark wrote to reflect what he called Coltrane's "open and free artistic philosophy." DownBeat's review noted that the opening track "sounds as if it could have emerged from Coltrane's late period," describing Clark as "a self-assured saxophonist with a vision that's in touch with the tradition, but not mired in it"; JazzTrail's review awarded the album a B+, calling it "wholly satisfying."

In 2020, at the start of the COVID-19 pandemic, Clark received a Chamber Music America New Jazz Works grant to support new compositions; he later served as a panelist for the same New Jazz Works program in 2023 and joined Chamber Music America's Jazz Think Tank on building music, community, and social change in 2025. He has continued to lead his own working quintet in New York, performing internationally at venues including Blue Note Beijing, Jimmy Glass Jazz Bar in Valencia, and Jazz Club Unterfahrt in Munich, and has shared stages with musicians including Billy Hart, Reggie Workman, Orrin Evans, and Billy Drummond. As of a September 10, 2025 performance at Smalls with trumpeter Wallace Roney Jr., pianist Theo Hill, bassist Conway Campbell, and drummer Kush Abadey, Clark remained an active bandleader working toward a third album built around his working quintet's own book of originals.

Clark's playing sits squarely in the "modern mainstream" idiom his own reviewers keep reaching for: a post-bop tenor style built on the John Coltrane Quartet and Miles Davis Quintet as reference points, filtered through a decade spent inside Rashied Ali's more open, free-time conception of time and structure. Jazzwise's Kevin Le Gendre, reviewing Judgment Day, Vol. 2, singled out that quintet as "proof positive that Ali... is a complete musician, one who shows that mainstream vocabulary is not beyond the reach of a master of the avant-garde" - a description that applies equally to Clark's own writing, which pairs conventional hard-bop structures with the loose, free-time trio writing of the "Mr. Ali" tributes on Inner Visions. DownBeat has called him "a self-assured saxophonist with a vision that's in touch with the tradition, but not mired in it." Beyond his own working quintet, Clark's catalog reflects a working New York sideman's range, from mainstream hard bop (Winard Harper, Greg Murphy) to the downtown avant-garde circle around drummer George Spanos.