Although my Moodle had been updated to 3.3, I had neglected to update the Moodle Mobile Additional Features plugin. Once this was accomplished, I was able to use the Lesson module within the app. My apologies to those who spent time investigating the problem on my behalf.
As far as I can tell, iframes do not display in the Lesson module when using the app (MOBILE-2144). However, it would be good if other users could confirm this using the module in their own Moodle installations.
P.S. - If you've noticed that the new 'course overview' doesn't appear as you expected within the app, update the additional features plugin. This will make it appear as it does in the Desktop version.