I'm running OS X Lion 10.7.5 on a 2011 Macbook Pro, how can I access OS X Mountain Lion v10.8?

You may be able to still buy the download code (for about $19) and use it to

then access Mac App Store to get the product. You have a process whereby

the code gained (by reply official email) can be redeemed. Mt Lion 10.8(.5)

may require subsequent visits to get later patches from Apple servers.

OS X Mountain Lion - Apple

If you need to purchase Mac OS X 10.8 Mountain Lion, you may order it from

this page. The current version of the Mac operating system is macOS High Sierra.

https://www.apple.com/shop/product/D6377Z/A/os-x-mou

Somewhere I have the URL to the Apple page for this item.

However, if your Mac can use Mt Lion 10.8.5, it may also

be able to use El Capitan 10.11.6 ~ and the latter is Free.

• How to download OS X El Capitan - Apple Support

Whatever your leisure, either takes some time to download as the files are large

~ so that means if you have wi-fi, the best way to download would be Ethernet.

Good luck & happy trails! 🙂

[edited to add two links]

You might be able to run a newer version of OS X than Mountain Lion.

What's your MacBook Pro model number? Apple Menu -> About this Mac

Also go to the App Store and see what options are available.