Lawrence had been at Newport County in a similar position.
"Over the last decade Lennie has worked with and improved a number of successful managers including Paul Trollope, Dougie Freeman and Michael Flynn," said Stevenage in a statement. "We believe this appointment is a positive step in helping us rebuild to gain success on the pitch."
Lawrence was director of football for a short spell at Hereford when Jamie Pitman was manager.
Meanwhile it is not known whether former Hereford FC manager Russell Slade is still at Stevenage. He joined the League Two club last February as a 'management consultant' after being sacked by Hereford in January.