The appointment follows the departure of several Lime staff, including head of experiential marketing Dale Barker to Iris Experience and business development director Luffa Khonm to Branded Moments of Truth.
Former Triangle managing director Cawley was made Arc deputy managing director after the merger of Triangle and Arc last year. Both are owned by Leo Burnett.
Arc managing director Mike Spicer handed the reins of the agency to Andrew Edwards, Leo Burnett's president for EMEA, in March.