Connection Apple TV to the analog audio stereo speakers

We had the same issue in our school environment, with teachers wanting to hook Apple TV devices to their projectors. Instead of buying new projectors, we used the Kanex ATVPRO, which allowed for both audio and video. This allows them to AirPlay from iOS or the MacBooks. We can also stream content from Netflix this way.

As for your specific configuration, I tried several combinations of digital optical to analog RCA, and never got what I wanted. Only the Kanex has worked for me.

If it works through the regular 30-pin to USB cable, it should work with the Lightning to USB cable as well.

This type of connection is through an all digital interface and I am not aware of any changes to it, when the lightning connector was introduced.

It's a different story, when you have a Y-Cable for your car. This would have a dock-connector on one side and a USB and Headphone-jack on the other.

In this case you will need a Lightning to 30-pin adapter. This would be an analog connection and the adapter would do the conversion from a digital into an analog signal.