Lipman graduated from the University of Toronto with a Bachelor's degree in 1960 and then went to Harvard University, receiving his master's degree in 1961. He then earned a Ph.D. there in 1965 under the supervision of Oscar Zariski (Quasi-ordinary singularities of embedded surfaces). In 1965 he was an assistant professor at Queen's University in Kingston and in 1966 was an assistant professor at the Purdue University, where he became professor in 1971. From 1987 to 1992, there, he was head of the mathematics department. He was a member of the MSRI and visiting scholar at the University of Cambridge and the University of Nice and a visiting professor at the Columbia University and Harvard University.
He specializes in singularity theory in algebraic geometry.
- Collected Papers of Joseph Lipman. Queen's Papers in Pure and Applied Mathematics, vol. 117, Queen's University Press, Kingston, Ontario, 2000.
- Editor with Herwig Hauser, Frans Oort, Adolfo Quirós: Resolution of singularities. A research textbook in tribute to Oscar Zariski. Birkhäuser, Basel 2000, ISBN 3-7643-6178-6. (Progress in Mathematics. volume 181.)
- Introduction to the resolution of singularities, in David Mumford Algebraic Geometry (Arcata 1974), Proc. Symp. Pure Math. 29, American Mathematical Society 1975
- Desingularization of two-dimensional schemes, Annals of Mathematics, volume 107, 1978, pg. 151–207
- American Men and Women of Science, Thomson Gale 2004
- Mathematics Genealogy Project
- List of Fellows of the American Mathematical Society, retrieved 2013-11-24.