I ran and built your test app on my iPad 4 with no changes. Here are the results:
Simulator (2906): worked (see 1st screen shot)
iPad 4 (iOS 9.3.2): worked (see 2nd screen shot)
So at this point since no fonts seem to work it has to be something local blocking it and I really have no clue what that might be… I’ll try to have a conversation with the engineers in a bit to see they have any ideas.
Does this font/method of loading work in other apps where you do have custom fonts work?
Can you do another test this time loading the font old school (include the UIAppFonts block in build.settings, load by Font Family name instead of file name) and see if that works?
Finally I noticed this in my log file:
Jul 26 10:56:33.548 Activated fonts in ‘Robotron.ttf’ (Robotron)
Jul 26 10:56:33.593 Copyright © 2009-2016 C o r o n a L a b s I n c .
Version: 3.0.0
Build: 2016.2906
Jul 26 10:56:33.621 Loading project from: /Volumes/Macintosh HD/Media/Downloads/What the Shell
Jul 26 10:56:33.622 Project sandbox folder: ~/Library/Application Support/Corona Simulator/What the Shell-BEA285BAA549719F01AEB0DF37AF1A03
Jul 26 10:56:33.657 Platform: iPhone / x86_64 / 10.11.5 / Intel HD Graphics 4000 OpenGL Engine / 2.1 INTEL-10.14.66 / 2016.2906 / en | US | en_US | en
Are you seeing that line?