User Agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/48.0.2564.116 Safari/537.36 Steps to reproduce: Received an email from Google Calendar about another user cancelling an event they had scheduled. Actual results: Email had a header from Thunderbird saying "This message contains an event that has already been processed". But the message had not been processed. The cancelled event was still in the calendar. Only after syncing the calendar did the event disappear. Expected results: Event should have immediately disappeared from the calendar and the today pane.
What version of Lightning are you using (look at the addon-manager)? Can you attach the email (not just the event but the entire email) with the cancellation? Are you using the Provider for Google or the built in CalDAV to sync with Google? In general, the event is not expected to disappear immediately, but a delete button on the blue bar and a different message text should have been displayed, at least until you synced your calendar with the server (because Google probably removes the event serverside).
Resolving incomplete. If this is still an issue for you with the latest TB 45.* / Lightning 4.7.* and you can provide the requested information, please feel free to reopen.