I wonder if there is a subtle difference between "lost child" and "missing child".
*Not a teacher
Yes, there is.
lost child = lost his custody, died in an accident or can't find him/her
She get the child's custody. He lost his child.
They lost their child in a car accident.
missing child = can't find him/her
He has been missing for several hours and nobody (or the ones who are looking for him) knows where he might be.