He was born in Oslo as a son of banker Jannik Lindbæk Sr. (1906–1966) and chief physician Ellen Margrethe Lund.
His aunt was journalist and war correspondent Lise Lindbæk, and he was a great-grandson of Elise Aubert In December 1963 he married teacher Grete Schjøttelvig.
He later received a Fulbright scholarship to continue his business studies for one year at the University of Kansas.
[1] Lindbæk became head of the Nordic Investment Bank in Finland in 1986, overseeing hundreds of millions in loans to develop the economies of the five countries that own the bank: Denmark, Finland, Iceland, Norway, and Sweden.
He was executive vice president of the International Finance Corporation in Washington, DC from 1994 to 1999.