Click on the gear symbol in the main menu (the settings icon), and see what options you have. If you click on the LINE login symbol, what happens for you?
You could try deleting the game app off your device, reinstalling it, and then entering in your normal login info. There really should be a "logout" feature in the settings. Since the save data is stored on some cloud service tied to your login account, deleting the app shouldn't erase any of your data.