Mac had High Sierra, had to install Lion from Internet Recovery into a new hard drive, can't install High Sierra
You should be able to do the following:


Launch the Mac App Store app
Select the Purchased tab
Look through your purchased items to find OS X Mountain Lion (Note: There's nothing stopping you from also selecting either OS X Mavericks or OS X El Capitan)
Now click on the Download option on the right of the listing


This will download the OS X installer allowing you to upgrade from OS X Lion. Once you're upgraded, you'll then have the option/ability to upgrade to macOS High Sierra.

NOTE: If you can't see your Purchased list, or download the item, make sure you're actually signed into your account (i.e. look under the Store menu).