Are all sentences below correct?

* I parked in the parking lot.
* I parked on the parking lot.
* I parked at the parking lot.

My understanding is that I can use "to park in" if the parking lot is indoors and "to park at" with any kind of parking lot, but I'm not sure if "to park on" is usual for both indoor and outdoor parking lots.
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> I parked in the parking lot.
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> 
> 

This is correct whether the parking lot is enclosed in some way or not (it doesn't matter). The use of "in" here generally means "within the borders of". This is also the same sense you would use when saying "I parked in a parking space" as well.

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> I parked on the parking lot.
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> 
> 

This is not common usage for parking lots. It's grammatically correct, but the use of "on" emphasizes the idea of "on top of", and most parking lots don't actually have a "top" (they're open-air spaces with no roofs), so it seems a bit odd to say this. However, it is common to say something like "I parked on the asphalt" or "I parked on the street", because those are flat things you can put a car on top of.

> 
> I parked at the parking lot.
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> 
> 

This is also fine. This is using "at" in the sense of a location which you went to and then you parked there.

In general:

* "in" is the most common way to say this, and you can use it really any time you are inside of some area with well-defined boundaries (e.g. "in the parking lot", "in the yard", etc)
* "at" is also fine, and would not sound particularly strange in most situations.
* "on" would sound strange to most people.
I think you use "to park in" both when it’s outdoors and indoors.

I have never heard someone saying "to park at" or "to park on".