He graduated early from the Loomis Chaffee School in Connecticut, according to the New York Times, and then went to Harvard, where he majored in mathematics and received his bachelor's degree in 1946 aged 18. He completed a master's degree there and also pursued a PhD at Columbia University, which he never completed.
He began writing lyrics while at Harvard to entertain friends.
Lehrer's most enduring songs include The Elements, a list of the chemical elements set to the tune of I Am the Very Model of a Modern Major-General from The Pirates of Penzance, Gilbert and Sullivan's comic opera.
Other fan fourites include The Masochism Tango, in which the singer extols his beloved's violent passions with the lyrics, "I ache for the touch of your lips, dear / But much more for the touch of your whips, dear..."
He was renowned for his darkly comic ballads, including the necrophiliac epic I Hold Your Hand in Mine, I Got It From Agnes - where he sang about the transmission of a venereal disease - and Poisoning Pigeons in the Park, which detailed the birds' apparent appetite for "peanuts coated with cyanide".
In 1953 he released Songs by Tom Lehrer, a record that was sold through the post. It became a word of mouth success and sold an estimated half a million copies. The BBC banned most of Songs from the airwes the following year.
Following the success of the album, Lehrer began playing in nightclubs in New York, Los Angeles and San Francisco, and at events for anti-war and left-wing groups.
He wrote songs for the US edition of the satirical British show That Was the Week That Was, which were were made into an album in 1965.
The highly controversial Vatican Rag, a Catholic hymn set in ragtime that mocked the Church, was featured among other songs that condemned nuclear weapons.
The most notable of these was We Will All Go Together When We Go, which includes the lyrics "Oh, we will all fry together when we fry / We'll be French-fried potatoes by-and-by / There will be no more misery / When the world is our rotisserie / Yes, we all will fry together when we fry."
He wrote for the 1970s educational children's show, The Electric Company, and in 1980 his songs enjoyed a revival when theatre producer Cameron Mackintosh staged the musical revue "Tomfoolery" featuring his work.
He also taught maths and musical theatre courses at the University of California from 1972 to 2001, according to the New York Times.
In 2020, Lehrer placed his song writing copyrights in the public domain, allowing anyone to perform, record or interpret his work for free. He also relinquished all rights to his recordings.
In a statement on his website at the time, he wrote: "In short, I no longer retain any rights to any of my songs. So help yourselves, and don't send me any money."
He also warned the website would be "shut down at some date in the not too distant future". The website was still live at the time of writing.