Students and staff who were also in the same areas as the positive cases will be given advice.
In a second email, Lamb confirmed the school would remain open under existing alert level 3 protocol and has undergone a deep clean.
Junior exams scheduled for Wednesday will go ahead, Lamb confirmed.
Earlier on Tuesday it was revealed a student at Pakuranga Heights School has tested positive for Covid-19 and was infectious while at school for a week.
In a letter posted to the school website, principal Fintan Kelly said the student was infectious at school from November 8 to 12.
The east Auckland school will remain closed this week. The school said it is working closely with the Public Health Service and Ministry of Education officials.
A number of Auckland schools have recently reported student or staff Covid-19 cases.
On Monday night, it was revealed a teacher at an Auckland Catholic girls' school who taught at the school three days last week has tested positive for Covid.
In a letter to parents last night, Baradene College confirmed the teacher was infectious while at the school last Tuesday, Wednesday and Thursday.
Western Springs College has also confirmed a student tested positive for Covid-19 and the student was possibly infectious while at school on November 9 and 10.
The only contacts being isolated, tested and monitored are the 16 students who were with the case at a party on Friday night, principal Ivan Davis said.
Meanwhile, Onehunga High School was closed on Monday and Tuesday after a student returned a positive result for the virus on Saturday.
In a notice to parents and staff, the school said the student involved was at school last week on Monday and Tuesday while infectious.
Thousands of students across Auckland are set to return on Wednesday with just four weeks of the school year to go.
Last week, Education Minister Chris Hipkins announced Years 1-10 students in Waikato and Auckland will be able to return to the classroom from November 17. However primary and intermediate pupils will go back part-time and schools will set their own hours.