How to download old version of Mac OS X that I own and App Store lists, but App Store refuses on newer Mac

If you need it for an older Mac, download it on that one.

No Mac OS will install on any machine newer than the OS, as the drivers for the hardware simply didn't exist at the time.

If you fake it by installing on an older machine then swapping drives, it will just fail to start up.

If you go to developer.apple.com/downloads you will find all downloads that Apple has available. Limit your search to the "OS X" category and you'll see downloads for all versions of OS X from version 10.3 to 10.6.

I'm guessing that 10.7 and up are missing because starting with 10.7, the OS was only available via the App store. Unfortunately, that means that you'll only be able to get the installer from the App store, and the only way I know of getting older version from the App store is if you have previously "purchased" that version and wish to download it again.