Sorry that you're getting an error "Unable to create directory. You do not have permission to save the file" while saving a file in Lightroom Desktop.
Which exact version of Lightroom Desktop are you using, and what is your macOS version? Where are the images located? Does it help to navigate Adobe Lightroom Desktop > Preferences >: Local Storage > Reset?
You likely have a permission issue at the drive or folder level. You will need to use the macOS to change the permissions for your User Account for that (and perhaps other) locations. If changing doesn't work, you may need to repair your permissions.