The 19-year-old, who has scored three goals in seven appearances for the Cumbrians, will stay at Brunton Park until 28 January.
"Tom has had a fantastic first month with us," manager Graham Kavanagh told the club's official website.
"We've all seen the quality and we know that there is plenty for us to work with.
"There are still areas he can improve on but he is exactly the type of player we want here with us. It'll be good to work with him again as go on through January."
Lawrence will be in the squad to face Sunderland in the FA Cup this weekend, subject to relevant paperwork being completed.