The 20-year-old is the nephew of former England cricketer David "Syd" Lawrence.
Lawrence was given a two-and-a-half professional contract by Cheltenham Town during the 2014/15 season, but left at the end of last season after one first-team appearance at AFC Wimbledon.
Whilst on the Robins` books, Lawrence spent time out on loan gaining experience with the likes of Cirencester Town, Oxford City and Bishops Cleeve.