The article, which you can read here, by Ben Smith and Anita Badejo, is quite well-done, especially considering they had so little material on the record (no pun intended) to work with. Needless-to-say, when one is trying to put together a biography based on little existing information, you draw conclusions which may or may not be accurate -- in this case, wondering why in the world he stopped performing in public 40 years ago. (The good fellow is now 86 years old.) From all I've read in the past, I think they stretch a few conclusions, but all things considered they do a very respectable job, given that the best they can do is piece together random bits and just postulate.
For something so richly comprehensive under the conditions, there are however some surprising omissions -- the song that the authors offhandedly mention in a four-word, throwaway parenthetical, “Hanukkah in Santa Monica” was, in fact, written for his appearance on the American Radio Company (Garrison Keillor's A Prairie Home Companion companion show) in 1990, a fact well-worth mentioning, particularly since they go to great lengths explaining that Tom Lehrer gave up public performing in the early '70s. I believe he even appeared on the show several times, and wrote three or four songs for it. It's surprising too that they didn't at least get any information from Garrison Keillor about working with him, since that would have been one of the few direct sources available. (It's possible they asked and got no reply, but given Keillor's love of talking about writers it doesn't seem likely.) Similarly, there's a paltry amount of first-hand information from producer Cameron Mackintosh who worked with Lehrer putting together a very successful stage musical revue of his work, Tomfoolery. Indeed, again, there's unmentioned footage of Lehrer performing on a 1998 TV special that honored Sir Cameron -- it was a rare performance, to be sure, but a very public performance nonetheless, long after 1972, and should have been referenced. And there also are videos online of Lehrer performing new songs in private venues, like at school functions at the University of California, Santa Cruz, where he was teaching. No, they aren't public performances, but very noteworthy.
To be clear, this isn't a criticism of the article, which as I said is very good -- most especially considering how little information there was to work with. But since it is so good and impressively researched, that's makes these notable omissions surprising.
Videos of Tom Lehrer happily do exist on the Internet, and I've even posted some on these pages, like here. But more difficult to find are those obscure, private ones. But obscure is our bread and water around these parts. So, here's one of them, a whopping 13-minutes long from 1997, and singing material you've likely never heard --