As previously suggested, make a copy of your current version of Logic, then either compress it into a .zip file or rename it Logic Pro X 10.2.2. You can move this onto your desktop if you'd like. This will preserve your 10.2.2 version, which you can drag back into your applications folder after updating.
I currently have three versions of LPX in my applications folder (10.2.4, 10.3.2, and 10.4.1) and can use any one of them at any time.
When you update LPX in the App Store it will not let you install a version incompatible with your OS, and should offer you the latest compatible version. See this thread:
https://discussions.apple.com/thread/7881698