Lubotzky is a mathematician working mainly in group theory and its connections with number theory, geometry, combinatorics and computer science. He is a member of the Israel Academy of Sciences and the American Academy of Arts and Sciences. Lubotzky has received several awards, including the Erdos Prize, the Rothschild Prize, the Israel Prize and an honorary degree from the University of Chicago. He has twice received ERC advanced grants. He was a member of the Israeli parliament from 1996 to 1999 and is currently the president of the Israeli Mathematical Union.