Since TB78 Lightning is always "installed" (integrated into TB), so this bug here can be closed. There is also bug 760412 which is about only showing the last text/calendar part of multipart/alternative.
To make it clear:
This bug here: Invite not showing when no Lightning installed. Bug 760412: text/html part not shown in multipart/alternative if text/calendar comes last.
Since TB78 Lightning is always "installed" (integrated into TB), so this bug here can be closed. There is also bug 760412 which is about only showing the last text/calendar part of multipart/ alternative. alternative if text/calendar comes last.
To make it clear:
This bug here: Invite not showing when no Lightning installed.
Bug 760412: text/html part not shown in multipart/