Steyn, who has amassed 694 Test points since making his debut in 2009 plays for French club Stade Francais, but as their season has already concluded, he is already back in South Africa.
Lambie will take a compulsory break of one week following his injury in Cape Town and will therefore miss the second Test match in Johannesburg on Saturday.
He underwent precautionary scans on Sunday, which proved normal, and he was examined for a third time on Monday morning by Springbok team doctor, Dr Konrad von Hagen. The player has already returned to his home in Durban.