Lawrence's university debut led on to the Edinburgh fringe, where he was runner up in the 2003 So You Think You're Funny competition. Subsequent wins of the Amused Moose Starsearch, York Comedy Festival New Act of the Year Competition and the BBC's New Act of the Year Competition in 2004 provided him further exposure on the UK comedy scene.
He presented his first hour-long comedy show at the 2006 Edinburgh Festival Fringe entitled How to Butcher your Loved Ones. It was nominated for the if.comeddie award (as it was known for that year only) for Best Newcomer. His 2007 Fringe show, Social Leprosy For Beginners & Improvers, was nominated for the main if.comedy award. He has returned to the Fringe every year up to 2015.
Lawrence has featured in numerous radio and TV shows, mostly as a stand-up performer. He has also appeared on television as a comic actor, playing the builder Marco in the BBC TV sitcom Ideal. He has written and performed four series for BBC Radio 4, most recently the 2015 sitcom There Is No Escape.