I've understood Apple's iOS USB mirroring protocol on Mac, yes, the one can be used to mirror iOS devices to a Mac desktop computer.
This project contains source code of the implementation for the same iOS USB Mirroring protocol on Mac, Windows, Linux, Android, Raspberry Pi, etc. With this independent implementation, iOS devices can be mirrored to any platforms using the lightning cable. No sotware is required to install to the iOS devices.
A screenshot is available here: (real time screen and audio streaming is supported).
https://plus.google.com/114395554184391775867/posts/N3pKpzK8A6K
This real. YouMap supports all kinds of mirroring protocols, AirPlay, Chromecast, Miracast, USB Mirroring, etc.