how do I get macOS version 10.8?

There are three OS's that are available for download, El Capitan, Sierra and High Sierra.

Depending on the model of Mac you have and its age you may be able to upgrade to High Sierra but as you are on Lion you would need to upgrade to El Capitan first. There are three links below with information on how to upgrade to each of those OS's and includes the specifications of Macs that can upgrade to each. You do not need Mountain Lion.

How to download OS X El Capitan - Apple Support

How to download macOS Sierra - Apple Support

How to download macOS High Sierra - Apple Support

If you're trying to upgrade to High Sierra, skip it and download El Capitan or Sierra from the Mac App Store instead.

If you're trying to upgrade to a different OS version, install it directly, using the links above if needed.

If you're using software not compatible with El Capitan or above, buy a download code for Mountain Lion from the Mac App Store.

If your computer's incapable of running El Capitan, it also can't run Mountain Lion.

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You can't unless you downloaded it in the past through the App Store. If so then you can re-download it from your Purchases page in App Store.

Otherwise, you need to have the installer saved on your computer or you can upgrade to the latest compatible version of macOS for your computer. The current version available is High Sierra. How to download macOS High Sierra.

Only by buying it via the Apple online store, NOT the App Store. If you are in the UK try here, OS X Mountain Lion - Apple (UK)

If you are not in the UK you will need to try you countries Apple on line store.

Why do you need Mountain Lion, you might be able to upgrade to another Mac OS like El Capitan, Sierra or High Sierra which are free and available through the App Store.

Where were you trying to download them from exactly?

macOS downloads don't require a previous version be installed specifically in most cases.

The few exceptions are that High Sierra does in fact require an update to El Capitan first if you are running Lion or earlier.

El Capitan can be installed directly from the Mac App Store on Lion, it should not require anything else.

If you are getting the downloads from somewhere else such as here: Apple - Support - Downloads you would be downloading system and security updates which require a base system already installed. i.e you cannot install the El Capitan 10.11.4 update without already having some version of el Capitan.

Downloading directly from the Apple Store will let you install the complete system if your Mac supports it.

If you tried downloading el 10.11 El Capitan from the Mac App Store and got an error stating your Mac is not compatible with it, then you cannot update your mac any further. Lion 10.7.5 is the last Mac OS version it supports. macOS versions 10.8, 10.9, 10.10 and 10.11 have the same system requirements.

A Late 2011 MacBook Pro can support High Sierra, but you'll need to download El Capitan first as has been said.

You can find el Capitan in the Mac App Store.

Follow the steps here: How to download OS X El Capitan - Apple Support

https://support.apple.com/en-gb/HT206886

As said in this thread already. 10.8 needs to be purchased from the Apple Online Store: Buy OS X Mountain Lion - Apple

There is nowhere else to get it from.

But you do not need to install 10.8. If your Mac supports it, you can install 10.11 el Capitan directly and for free.

What exactly is the error message you are receiving when trying to install El Capitan? You can follow the steps here to get El Capitan: How to download OS X El Capitan - Apple Support

What model of Mac do you have exactly?

As I said you do not need to install 10.8. As you are on Lion you cannot upgrade directly to High Sierra, you upgrade to El Capitan Sierra and then you can upgrade to High Sierra. See the links above. No need to purchase 10.8 Mountain Lion.

In the App Store when you select Updates it searches for updates for the Mac OS you are running.

Moving from one OS to another is called an upgrade, a subtle difference.

I have the same issue as Sandyland67. All updates are blocked (including El Capitan) and say they are not possible without having OS 10.8 first, however it appears I cannot find this update anywhere, it seems impossible to go from 10.7.5 to10.8.

You can buy it from Apple's Online Store at OS X Mountain Lion