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: 
A school lunch can either be:

* a lunch prepared and served in the school cafeteria, or
* a lunch prepared at home and taken to school to be eaten there.

When I hear the term "school lunch," I typically think of the former meaning first. However, as was stated in a comment by @userr2684291, the latter meaning is still valid. (Just because a phrase **usually** means one thing doesn't mean it **never** means another.) Here are a couple quotes that use the term in this way:

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> *When I was in the second grade, my mom packed my school lunch every day in a brown paper bag*. (Aegina Angeliades, *My Skin Don't Fit*, 2014)
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> *If you need fresh ideas for making healthy school lunches, leftovers can save the day*. ([VegKitchen website](http://www.vegkitchen.com/recipes/leftover-heaven-ideas-for-school-and-brown-bag-lunches/))
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As a footnote, you should remember that any two-word term like "school lunch" may have more than one meaning. Moreover, when you say "in American English," you should know that [**regionalisms** may and often do apply](https://en.wikipedia.org/wiki/Regional_vocabularies_of_American_English#Regionalisms). 

*Hotdish and a frappe for lunch, anyone?*
***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)

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> 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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