I would not be surpried if Apple doesn't provide this as composite connections may be considered too out of date to support. The good news is there are very cheap adapters to convert a VGA signal to a composite video and Apple now has a Lightening to VGA adapter. Audio can be carried with a headphone to RCA adapter cable.
VGA to Composite Adapter - http://www.newegg.com/Product/Product.aspx?Item=N82E16815276011
Headphone to RCA Adapter - http://www.yourcablestore.com/6-Foot-35mm-Stereo-Headphone-To-RCA-Adapter-Cable_ p_29.html
It is going to cost more than a stand alone cable but the good news is both the VGA and headphone adapters have uses beyond the iPad. I'd be willing to bet you already have a headphone to RCA adapter laying around somewhere as many devices come with them.
If Apple doesn't release a composite video adapter for Lightening, this will be the cheapest route. HDMI to composite is also possible but is more expensive.
You may want to use lighting to HDMI then convert the compsite (yellow/video red and white right/left sound). This will send sound and picture to the T.V. I've done it in my car and works great!!
EDIT: Sorry didnt see you don't have HDMI..