His grandparents, participants of the 1863 uprising, were exiled from Lithuania to Russia. Born in 1918 Kazickas and his family returned to Lithuania in 1922. Later, in 1937-1940, he studied economics in Vytautas Magnus University and in Vilnius University. During the Second World War, in 1944, Juozas Kazickas and his wife Aleksandra moved to Germany and later to the US. In 1951 Kazickas defended his thesis in Yale University. He worked in Georgetown University and as the advisor to the US Departments of Defence and State.
During the occupation of Lithuania Kazickas family fostered the Lithuanian culture. He joined the Lithuanian Foundation in Chicago and had been its director for 16 years.
After leaving academic activities Kazickas was engaged in coal and oil trade. He established a company Neris and became a prosperous businessman. Kazickas worked as a consultant for various companies and governments (mostly for India). He was also a shareholder and director of investment funds and banks. After 35 years he returned to Lithuania and in 1991 established Litcom (now Omnitel), the first private capital and telecommunications company in the Baltic States. The businessman also attracted numerous major investors from the US: Philip Morris, Coca-Cola, Motorola and Williams concern. Kazickas fostered Lithuania's independence: consulted the Government, organised meetings between leadership of Lithuania, the US and countries of Western Europe.
After retiring from active business he was engaged in charity and support projects. Kazickas Family Foundation, founded together with daughter Jurate, supports education programmes in Lithuania by supplying schools with computers and holding computer programming courses for school students.
Kazickas was decorated with the Riflemen's Star, the Commemorative Medal of 13 January, the Cross of Commander of the Order of the Lithuanian Grand Duke Gediminas, the Grand Cross of the Order of the Lithuanian Grand Duke Gediminas, and the Grand Cross of the Order for Merits to Lithuania.