Integrate Lightning (Tunderbird AddOn) into Yosemite's Notification Center

I currently went from Mac OS X 10.6.8 Snow Leopard to 10.10.2 Yosemite. I am kind of impressed of the "new" Notification Center" and asking myself if there is any way to integrate Thunderbird's Lightning Calendars and Tasks into this.

Incoming mails are integrated like a charm. However, my calendars aren't.

I could use Apple's Mail and Calendar Apps for sure, but I'd rather use Thunderbird for seamless integration in my Linux-Windows-Mac-based Workflow.