If it's a public parking lot, I guess that means you can go park your car there for free too!
All something being "public" means is that you have access to it. This doesn't mean it has to be free. Otherwise all pay parking lots would be illegal, all road tolls, San Francisco would owe over a zillion dollars in refunds for the Golden Gate Bridge's toll, etc.. You pay for the right to drive a car on a public road when you pay for your registration. Sometimes the upkeep of public property is assessed to those who actually use it rather than making everyone pay for everything they don't use.
Oh, and if the school is a public building, then I guess the theater should be free for anyone to use, as should the gym if someone wants to have a weekend kegger!! Amirite?