The 34-year-old Trinidad and Tobago defender who joined the Railwaymen at the end of September and made his debut in the 3-1 defeat against Northampton Town.
Since then Lawrence has made 11 apperances for the Alex and has impressed in recent games.
With Lawrence signed up to the end of the season, Swansea have given permission for him to play against Millwall this Saturuday in the FA Cup.
The Swans defender is out of contract at the end of the season at the Liberty Stadium.