Will a 30 pin to composite cable work with a lightning to 30 pin adaptor?

Hi - this article may help - http://www.imore.com/lightning-connector-drops-video-out-support-wants-you-use-a irplay-and-apple-tv

Absolutely not. Apple sees composite and something out of the 18th century...somehting dirty peasents would use. So...you'll need a new HDMI TV and Apple TV. That's the only solution (or a few hundred bucks in ridiculous cables, adapters, and convertors).