Question: What does "school lunch" mean in American English? Is it ambiguous between a lunch provided by a school and a lunch prepared at home like a bag lunch?

Answer: 
***School lunch is the meal eaten at school.***

Now here in this sentence it doesn't say anything if the lunch is provided by the school authority or prepared at some other place with the objective of eating it at school.

[![Home made school lunch](https://i.stack.imgur.com/Yf7tW.jpg)](https://i.stack.imgur.com/Yf7tW.jpg)

So the school lunch is the typical lunch that is packed at home to be eaten at school, or provided by the school itself to be eaten at lunch break at the school.

[![Lunch on a tray with compartments](https://i.stack.imgur.com/IWVoc.jpg)](https://i.stack.imgur.com/IWVoc.jpg)

> 
> It's estimated that 30.6 million students in the US get their lunches
>  in the school cafeteria versus bringing it from home. (*[Source](http://www.businessinsider.com/school-lunches-in-the-us-compared-to-other-countries-2015-2 "Here's how school lunch in the US stacks up against what's served in the rest of the world")*).
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To add on to the other answers: "School lunch" is ambiguous. It could be provided by the school for the midday meal, or one that you bring with you to eat at school. Without context, you don't know for sure which is meant, or even if there is any relevant difference.

In addition, "school lunch" (commonly "lunchtime") can also be the *time period* during which students normally eat the midday meal, and then go play or talk or whatever else they are permitted to do during that break time. Example:

> 
> Mister Potter. As you have been told, **school lunch** is for eating or playing with your friends. It is not for drawing magic circles and transforming your fellow students into newts. We are not that kind of school.
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Again, context is important to understand which is meant.