If you're using a Mac computer, connect your iphone to your Mac via the Lightning cable.
Then open Quicktime player
Select file, new movie recording.
Then click on the little arrow to the right of the record button and choose the video and audio source as iPhone.
If you're having issues with lag (if you're on an older Mac,) try setting the quality lower.
Some tips.
Double click your iPhone's home button and clear out any programs. It will free up memory for the one you want to record.
Shut down other applications on your Mac, it's best if you're only running Quicktime on your Mac, and the program you want to record on your phone.
I do this on my 6 year old Macbook Pro and the results are pretty good! Here's an example.
https://www.youtube.com/watch?v=Chg-C8xBKWY
Hope this helps.