db={col1:[{_id:"st_123",stud_num:123,school:"sc_123",gender:"M"},{_id:"st_234",stud_num:123,school:"sc_234",gender:"F"},{_id:"st_345",stud_num:123,school:"sc_345",gender:"M"}],col2:[{_id:"f_123",stud_health_id:"st_123",schoolYear:"sy123"},{_id:"f_234",stud_health_id:"st_234",schoolYear:"sy234"},{_id:"f_345",stud_health_id:"st_890",schoolYear:"sy234"},{_id:"f_456",stud_health_id:"st_345",schoolYear:"sy345"}]}

db.col1.aggregate([{$lookup:{from:"col2",as:"col2",let:{schoolYear:"sy234",stud_id:"$_id"},pipeline:[{$match:{$expr:{$and:[{$eq:["$schoolYear","$$schoolYear"]},{$eq:["$stud_health_id","$$stud_id"]}]}}}]}},{$match:{"col2.0":{$exists:false}}},{$unset:"col2"}])