He has made 20 league appearances so far this term, with Lawrence confident the Pirates will be able confirm the deal in the coming days.
"We have almost reached agreement with Byron, there are just one or two fine points which are holding things up," Lawrence told the Bristol Evening Post.
"But we are confident we will be able to conclude things satisfactorily.
"I have known Byron since he was a youngster at Cardiff and we feel he has progressed during his time with us."
Source: Team Talk