I think you're close in your first suggestion, but it's not so much that the lost prophet's words are unheeded so much at it is that his words are unappreciated, or not understood, especially at the time of their utterance.
Quite often, a lost prophet's contemporaries can't comprehend his message, so they don't recognize his brilliance; to many, he seems merely wayward and confused. Later on, though, people begin to recognize and appreciate his genius, and thus the label is bestowed as a belated compliment.
In the Economist article, the author is talking about conversations that foster and refine major ideas – whereas such conversations were once largely confined to university campuses, the online environment now allows more people to participate. But this wider audience is a mixed blessing: for every brilliant recluse there is a shallow curmudgeon.
The back-and-forth between bloggers resembles the informal chats, in university hallways and coffee rooms, that have always stimulated economic research, argues Paul Krugman, a Nobel-prizewinning economist who blogs at the New York Times. But moving the conversation online means that far more people can take part. Admittedly, for every lost prophet there is a crank who is simply lost.
In this case, the label lost prophet is not so much being bestowed belatedly by historians, but applied to one who has perhaps had the keen insights all along, but, until now, had never been granted a seat at the table. But, as the article implies, that next person pulling up a chair could be a keen savant – or could be a blustery know-it-all instead.
The term lowest (or least) common denominator (LCD) of a set of whole numbers (i.e., non-zero integers) is the smallest whole number that each member of the set divides evenly. Mathematically, this means that the LCD includes all the factors of each member of the set, but in the vernacular, it means the smallest thing that a group of people share, an idea akin to the smallest prime factor shared between whole numbers, a concept void of mathematical utility. The attraction of the misnomer is likely the pejorative use of lowest, the sharing aspect of common, and the meaning of denominator as a namer, labeler, or classifier.
In Hawking's case, he's talking about knowledge, saying that when Trump speaks to people he's talking so that the least knowledgable (or equivalently, the most ignorant) will approve. One of those most ignorant is Trump's campaign manager, who instead of admitting that he and Trump's partisans don't understand Hawking because they're ignorant, instead claims that Hawking is unintelligible.
Best Answer
To wax rhapsodic about something is a common idiom meaning to praise something excessively.
As James indicated, the verb to wax is a verb meaning to grow, but the verb is very uncommon outside of a few contexts such as this idiom, and when speaking of the phases of the moon.