With the landing of bug 373380, Lightning will now attempt to send invitations to any attendees you may have added to the attendee list of your event. These invitations have been tested with the latest versions of iCal.app and Outlook. We'll be testing with Zimbra soon. This functionality will be in the upcoming 0.5 release.
While we don't currently handle the reply you get back, other than as if it were just a normal email message, support to do so is already written into Sun's prototype event dialog, which we hope to migrate to fairly soon, most likely after 0.5 ships.