Okay so I retried what you did turned everything off and reset it. Some weird things happened. 1st, I got picture. But it was breaking up horribly it never stayed true once. And then I turned it off a few times kept getting the scraggly lines and a faint picture. Then I tried doing it again and I got a QR code come up on the screen in the HDMI input.
that might be an issue with video display from the Parrot Bebop. Wifi video connections aren't the greatest, and tend to lag horribly. I had a Blade Glimpse that had Wifi capabilities to capture pictures and video in flight, but it was consistently 1-2 seconds behind the movement (when it actually managed to connect up).
It could be either connection, or possibly that the app itself will not allow output through the lightning to HDMI adapter, for HDCP (High Bandwidth Digital Copy Protection) reasons. Can you connect your phone through the adapter to a TV, and does that work? Have you tried connecting say, a DVD/Blu-Ray player to your goggles to see if a video feed comes through via the HDMI?