Does the app show any other error? I wonder if perhaps your iOS purchase is linked to another Lightroom account, not the account you were signed into. If so, an error would mention it the problem is due to duplicate purchase.
If that's not the problem, can you try force-quitting and relaunching the app? Also, we released an app update today. If you search for Lightroom on the iOS App Store, you will see the option to update. Does the app update help?