Apart from Lawrence, centre Oscar Beard and hooker Luke Cowan-Dickie have also been withdrawn.
England have called up Max Ojomoh, Will Muir and Jamie Blamire to replace them.
"Beard will travel to England's training base in Girona where he will continue his return to play protocol," the RFU said in a statement.
Lawrence, who has earned 21 caps for his country and scored two tries, was expected to start in England's Six Nations opener in Rome against Italy on February 3rd after a strong season with Bath.