The Soca Warriors needed to avoid defeat to have any chance of progressing to the quarter finals following draws against Honduras and Panama, but went down 2-0 to the South American side in searing heat in Miami.
The news will please Wrexham boss Denis Smith, who was initially concerned about the lack of rest time Lawrence would have over the summer due to international committments.
It is expected now that Lawrence will be given some time off to rest after a busy season for the big defender, joining up with the rest of the Wrexham squad at a later date.