The 24-year-old has joined after playing Evo-Stik League Premier Division football with Frickley Athletic last season.
Primarily a central defender, Lawrence, who also turned out last season for Worksop Town, is also capable of playing central midfield or centre forward.
Lawrence is not the only player to have joined from an Evo-Stik Premier club, for Shomari Doyle has also signed up after being with Buxton last season.
Meanwhile left back Brad Wilson has rejoined the Wrens after a year with AFC Mansfield and, as manager Craig Denton looks to tighten up a defence which conceded too many goals last season, he has also recruited former Sheffield back player Tim Whittaker from Hallam.
Goalkeeper Ben Townsend is one of five of last season's squad to have signed up for this season, along with Jordan Claxton, Tomas Poole, Rob Ludlum and Ryan Herbert.
The new look side will face their first match action on Friday when they visit Ollerton Town for a pre-season friendly.