It would be fantastic if the Noise can record a live performance in an audio file format.
Thanks for sharing this request, and I can see how this would certainly be useful.
For now, there are a few ways of recording a live performance of NOISE.
You can, for example, connect the headphone output of your iOS device to a microphone/audio input on your computer or audio interface (if present), and then use a DAW to record this audio.
If you have a Mac, one way connect an iOS device to a Mac using a Lightning-to-USB cable and follow the steps mentioned in this forum post. (You can also use a different DAW than Logic in this case.)
You can also record from an iOS device to a Mac as an M4A file by following these steps: