This might be because the game does not have the necessary permissions to send you notifications. To fix this, go to your device's Settings app and find LEGO® Star Wars™: Castaways. Select this option, and in the app Settings, find the Notifications option, and make sure "Allow Notifications" is on.
My Game Center friends have tried to invite me while I was offline, but I don't see any notifications on my phone.
Last Updated: 475d