Purchase Logic Pro X under new license

No worries, glad to help. Preferences and presets are not affected if you just remove the app, because they are stored in different locations (preferences in [Your user name]/Library/Preferences, and your custom presets in [Your user name]/Music/Audio Music Apps. Sound Library and its presets reside in [Your System HD]/Library/Application Support/Logic (unless you relocated it to an external HD).

Hi Alex, you may have to purchase Logic, which would then be associated with your own Apple ID. This is done using App Store app where you log in with your own Apple ID, then look for Logic Pro X app.

However, as you have Logic currently installed, you need to zip the app in /Applications folder and move the archive to another folder, then delete the app (move to Trash > Empty Trash). That is, if something goes wrong, it's best to preserve the working version of the app (you will be able to extract it back to /Applications, if need be).

This should trick App Store into "thinking" the app isn't installed, and you will be able to download and install new version of Logic in App Store after making the purchase.