I find myself with this problem as well. This is a recent problem though, only in the past two days. My Lightning adapter in my car has been working flawlessly for over a year. Only within the past two days, does it refuse to play music from my iPhone through to my car. Occassionally, as the device is registering with my car, a brief amount of audio will transfer to my car speakers but it will stop within a second and only be playable through my phone. The phone is still being charged when connected, though.
I tried to see if there was an overnight automatic update of my phone, but didn't see anything in my history list. Briefly received a message on my iPhone "...not supported..." when connected, but it dissappears within 2 seconds so I can never read the whole thing. Does not reliably appear.