Yes - that would be my interpretation too. "To wax lyrical" is a kind of set phrase meaning to talk and talk in an over-blown way about something, so I think this is a jokey adaptation of that saying. I also agree with Bibiolept's comment.
The problem with this author is that he provides little context for some of his playful lines, so I'm often forced to guess what he means.Please provide context and background, october 15.
While you are, of course, absolutely right about what 'wax' really means, since phrases like "wax poetic" and "wax lyrical" tend to involve the person blathering on for a while, I suspect the author did mean something like "to speak ignorantly" rather than "to grow ignorant".The word "wax" means to grow, or increase, or to become to a greater degree. A moon waxes during the first part of the lunar month when it increases in size. To wax fat means to grow fatter. To wax lyrical means to stop being prosaic and to become lyrical instead. To wax ignorant, if it means anything (and I am not sure it does) would mean to become increasingly ignorant.