The Cowboys used their second first-round pick on the UCF defensive end at No. 23 overall. Dallas moved from No. 20 to No. 23 in the deal with the Eagles, who selected USC wide receiver Makai Lemon.
Lawrence, 22, had familiarity with North Texas, as he played in the East-West Shrine Bowl at The Star in Frisco in January. Lawrence also had a good relationship with Cowboys assistant defensive line coach Demeitre Brim, who was a defensive analyst at UCF last season.
Staff writer Joseph Hoyt contributed to this report.