While all of his songs are funny, not to mention incredibly quotable, his live albums include a few moments that have the audience laughing so hard that Lehrer actually has to stop and wait for them to calm down. Most infamously, from Bright College Days:
Lehrer: Soon we'll be out, amid the cold world's strife/Soon we'll be sliding down the razor blade of life... Audience: [loses it] Lehrer: Ready? Audience: [loses it again]
There's also his announcing of the song Oedipus Rex, which involves a lead-up of him describing how motion pictures have songs released with them. He then starts talking about the recently-released movie of Oedipus Rex, and then says "This film was not a financial success, and I believe this is because -". He got that far before everyone burst out laughing, at which point he said "You're way ahead of me on this one".
Another has Lehrer recount a novel a friend of his wrote, "about a young necrophiliac who finally achieved his boyhood ambition by becoming coroner." This only drew a few chuckles, but his next line brought the house down: "The rest of you can look it up when you get home."
Lehrer's appearance in the Cameron Mackintosh tribute concert "Hey Mr Producer". He makes his entrance at the piano, on a moving platform. When it comes to a stop, he remarks "they promised me seatbelts". He then credits himself for Mackintosh's success, saying "the combined profits of Cats and Tomfoolery" made Cameron into the man he is today". When talking about Mackintosh's rags-to-riches story, he said "even then, he had exquisite taste in rags". He then goes on to perform Poisoning Pigeons in the Park, to an audience that includes the Queen of England.
The Irish Ballad, about a girl who murders her family:
"And when at last the police came by Her little pranks she did not deny To do so she would have had to lie And lying she knew was a sin."
Most of In Old Mexico, but especially:
The mariachis would serenade And they would not shut up 'til they were paid
The Vatican Rag. For example:
Get in line in that processional Step into that small confessional There the guy who's got religion'll Tell you if your sin's original.
Also, the introduction - "I have here a modest example..." Tom Lehrer has never provided a "modest" example of anything in his life and his audience knows it.
Heck, the audience goes to pieces the very instance he announces the title!
"I am never forget the day I am given first original paper to write. It was on an analytical algebraic Euclidian metrization of infinitely differentiable locally Riemannian manifold; боже мой! ...This I know, from nothing."