Thanks for all the answers! I think I should specify the use case much more clearly. Sorry for not having done this earlier.
Use Case 1:
When I connect the iPhone to the receiver I can use the Lightning to USB, because the receiver has a female type A, just like e.g. a PC or like the charger. So I would agree that the Receiver must be the USB host, and the iPhone the USB device. This works just fine in my case, with iPhone and iPad.
In this case, the audio goes from the device to the host, or "Audio-in".
Use Case 2:
A friend of mine has a small device that converts USB to Toslink. This thing has a female Mini USB Type A, which is typically used at the receiving side of a USB connection. This device can be connected e.g. to a Mac, and then the Mac can output audio via this device to receiver which accepts optical Toslink signals.
In this case, the audio goes from the host to the device, or "Audio-out".
It is this use case 2 that I am unsure about:
a) Can the Lightning to USB cable be used in this case (assuming that I find the necessary non-standard adapters to actually connect the USB ports)? This would mean that the iPhone can act as a USB host with the Lightning to USB cable.
b) I know that the Lightning to USB Camera Adapter does convert the iPad into an USB host, otherwise it could not read data from a camera. So could this adapter also be used to produce "Audio out" to a USB device that supports receiving music?
If yes, would this also work with an iPhone (as pointed out in another answer, the iPhone does nor support reading pictures from a camera)?