What is the ruling on buying Ramadan lanterns for children to bring joy to them, and is this considered compensation for a potential feeling of deprivation a child might experience if he does not own a lantern like his peers?

There is no impediment to buying a lantern in Ramadan (definition) or at other times, because it is not intended as an act of worship, nor is it a custom exclusive to non-Muslims, nor does it contradict the doctrine of monotheism, provided that it does not include forbidden things like music or prohibited drawings.