I don't think terminating him would be a ethical way to handle this. Ask the parent to make the child understand that lying is a sin. If he still continue to do that, ask the parent to take him to a child psychologist. That should solve this problem. He is after all a child and it is not fair on your part to terminate him from your daycare where kids get their first grooming. Make sure that the parent knows the scene. Have a word with her.