Upgrade from Lion to Mountain Lion but not Mavericks I have to downgrade from Mavericks to Mountain Lion due to some software required for work. I used the Internet Recovery method to downgrade, but it is not Lion. I would like to upgrade to Mountain Lion, but there is only Mavericks available in the Mac App Store.
You can purchase OS X Mountain Lion still via Apple online:

Buy OS X Mountain Lion

Once you buy it for $19.99 they will send you an App Store link.