I've copied a great website below. I'm a teacher and this is the site that our school nurse uses for families. Also, I've been there with my own daughter. It's not the end of the world and all the cleaning is over the top!
Lice crawl from head to head ...they like a food source and hold tight to the person's head, trying not to fall off into your pit
That being said, there is no need to overreact or stop using your pit!
The bug can live off the host for 48 hours at most. Without a food source, it will die after that.
And yes, it is possible, though unlikely, that an egg will hatch if it has fallen off the hair shaft.
What you have to do is consider the odds....one or two bugs have fallen off said child into, say, the pit. The odds that another child will come into contact with that bug are slim!!
I would notify the families of children in that class. They are likely very used to getting letters like this from school.
Vacuum your gym floor if that makes you feel better
Here's the reality...the child had lice at least the previous week and you didn't do anything different in your gym.
Don't overreact.
The child who has the lice should be treated and the parent should continue checking for a month! that is key!
www.headlice.org
Hope this helps!