Lichtenbaum was an undergraduate at Harvard University (bachelor's degree "summa cum laude" in 1960), where he also obtained his Ph.D. in 1964 (Curves over discrete valuation rings, American Journal of Mathematics Bd.90, 1968, S.380-405).

Since 1990 he is professor at Brown University, where he was chairman from 1994 to 1997.

He was also a visiting scientist at Institute for Advanced Study (1973, 1984), University of Paris (VI, XI, VII, XIII), IHES (1974, 1977, 1982 / 83, 1987/88, 1997), MSRI (1987), Isaac Newton Institute (1998, 2002).

Since 2003, he has been an associate professor at the University of Paris Chevalaret.

[1] The Quillen-Lichtenbaum conjecture (from about 1971) about the relationship of the values of the Dedekind zeta function of number fields at specific locations (negative integers) is named after him and Daniel Quillen.