I'm using Lightning synced with Google Calendar for some time without any previous problems. As invitations received by e-mail were not showing in my Calendar, within Lightning I changed the Calendar properties for the Google Calendar so that the setting for E-mail was changed from 'none' to my e-mail address. This means that e-mail invites now appeared in my Calendar. However, for e-mail invitations from others that i accept I now appear to be shown as the organizer (even though I am not). Other invitees are now seeing me as the organizer and I receive e-mail notifications of acceptances and declines. I'm not sure if this is a Lightning or Google issue.