Lightroom app camera on iOS not recording location data

Actually, before trying any re-install, let's first check something simple:

1. in iOS Settings > Lightroom, is Location set to While Using (Allow location access)?

2. inside Lightroom's camera settings (which are opened when you tap the 3-dot menu inside the LR Camera) is "Geotag Photos" enabled?

I hope this is all you need to get this working as expected again.

In case that doesn't help, and you want to try reinstalling, here's more info to answer your last question: 

After any new install, the app will sync your account and image info, but not actually store all your photos on your device.  Thumbs are really all that's synced to your phone while you browse your account.  So a clean install of the app should take only minutes to sync your account to your phone.

If you edit images, high res copies or originals are then downloaded from cloud storage, but we have logic in place in our app to clean up such large copies of your images from the app cache when necessary, since all your files are synced to cloud storage.