On my iPad, latest iOS, when I try to update Lightroom mobile, I get this error message: "This app is not compatible with your device." I tried to delete LR and reinstall from the App Store. Same thing--will not update.
The default settings from Apple is to automatically install apps on your other devices. If you install from your iPhone, your iPad will try to download automatically. Make sure you're running iOS 10 or later and then please go to the App Store and make sure you're installing the iPad version.