I've had this happen with a cheaper non-offical apple lighting to 3.5mm, The system sounds would play through the headphones (message alerts ect..) but no music or video audio.
I tinker with electronics and when I opened it under my magnifying glass I found one of the wires wasnt connected to the DAC properly.
I understand some complaints about the 3.5-lightning interns of price and you can get working knock-offs but just do what I did and get either the official apple unit or a 3rd party one from a reputable 3rd party retailer as its worth it for the after sales support.......Just keep the receipt for it
If it is a legit apple supplied product then disregard that.
:)