If you have iOS 6 or later, please tap the Settings icon on the home screen of your device (not the one in the game), then open the Facebook section. Scroll down the page to the "Allow this app to use your account" section and check for Lucky Slots. Is the switch set to "No"? If this is the case, please set it to yes and reopen your Lucky Slots App to try again.
If that is not the reason, your authorization token from Facebook may have expired. This often occurs when you change any of your account information, like your password. We usually save that token to make the game startup easier, but there is a way to reset it. Please make sure you are logged into your Facebook mobile app, then try fully restarting the Lucky Slots app:
Double-click the Home button, then touch and hold an icon until they all start jiggling. Tap the red circle on the app you want to quit, then double-click the Home button to return to the Home screen and relaunch it.