How quickly can lice spread from one child to the next in school?

Very. A single close contact is all it takes children with lice are highly contagious and need to be treated successfully before they go back to school.
Quickly. Because children are in close contact with each other during play and other activities lice can spread pretty quickly through a classroom or school. In addition, child tend to share personal items such as hats, headbands, etc. The key is to check you child's head frequently if you are notified from the school that lice is "going around".