Lorenz was born in Hackensack, New Jersey and is an alumnus of North Junior High School in Newburgh, New York (where he starred in student productions), Carnegie Tech and Pratt Institute. His first published cartoon appeared in Colliers in 1956, and two years later he became a contract contributor to The New Yorker, which has published more than 1,600 of his drawings. He was The New Yorker's art editor for 25 years, from 1973 until 1993, continuing as cartoon editor until 1997.
He is a musician who plays cornet with his own group, the Creole Cookin' Jazz Band.
Lorenz is seen drawing in Lyda Ely's documentary film Funny Business (2009) which visited the studios of 11 cartoonists for The New Yorker.
- Here It Comes (Bobbs-Merrrill Co., Inc. 1968)
- Now Look What You've Done! (Pantheon, 1977)
- Hugo and the Spacedog (Prentice-Hall, 1983)
- The Golden Age of Trash (Chronicle Books, 1987)
- The Essential George Booth" (Workman, 1998)
- The Essential Charles Barsotti" (Workman, 1998)
- The Art of The New Yorker 1925 -1995, (Knopf, 1995)
- The World of William Steig (Artisan, 1998)
- The Essential Jack Ziegler (Workman, 2001)
- Big Gus and Little Gus (Prentice-Hall, 1982)