Lu Jeu Sham's family was from Fuzhou, Fujian, but he was born in British Hong Kong on April 28, 1938. He was graduated from the Pui Ching Middle School in 1955 and then traveled to England for his higher education. He received his Bachelor of Science in mathematics (1st class honours) from Imperial College, University of London in 1960 and his PhD in physics from the University of Cambridge in 1963. In 1963–1966, he worked with Prof. W. Kohn as a postdoctoral fellow at the University of California, San Diego. From 1966 to 1967, Sham worked in University of California, Irvine  as assistant professor in Physics and from 1967 to 1968 in Queen Mary College, University of London as a Reader. He joined the faculty of University of California in 1968. Sham was a professor in the Department of Physics at University of California, San Diego, eventually serving as department head. He is now a UCSD professor emeritus.
Sham was elected to the National Academy of Sciences in 1998.