Born in Oshkosh, Wisconsin, to Orthodox Jewish parents who were Lithuanian immigrants, Marovitz grew up in the Maxwell Street area of Chicago, after his parents moved to Chicago in 1910. Marovitz spent his youth selling newspapers, delivering groceries and prizefighting. As a teenager, he also worked as an office boy for a law firm, where a partner encouraged him to attend law school (and agreed to fund his tuition), even though Marovitz did not have a college degree. "In those days, you didn't need a college degree to go to law school," Marovitz later said. "So that's how I wound up the only sitting federal judge who never went to college." Marovitz earned a law degree from Chicago-Kent College of Law in 1925 at the age of 19, and he was at that point still 20 months too young to sit for the Illinois bar exam, which required all test-takers to be 21 years old. Marovitz took the exam when he turned 21, and passed it on his first try.
From 1927 until 1933, Marovitz was an assistant state's attorney in Cook County, Illinois. He then worked in private legal practice in Chicago with his brothers, Harold and Sydney, from 1933 until 1950. Concurrently, Marovitz was an elected member of the Illinois State Senate from 1939 until 1950, becoming Illinois' first-ever Jewish state senator. In 1950, Marovitz became a Superior Court judge in Cook County. He served as a Superior Court judge until his appointment to the federal bench in 1963.
In 1995, he received the Chicago History Museum "Making History Award" for Distinction in Public Service.
On July 16, 1963, President John F. Kennedy nominated Marovitz to a seat on the United States District Court for the Northern District of Illinois vacated by Julius H. Miner. The United States Senate confirmed Marovitz on September 25, 1963, and received commission on October 2, 1963.
Marovitz assumed senior status on his 70th birthday, on August 10, 1975.
Marovitz never married. One of his nephews, William A. Marovitz, later became an Illinois state senator himself and was married to Playboy Enterprises chief executive officer Christie Hefner.
Marovitz died on March 17, 2001 of kidney failure at his home on Chicago's North Side. In 2003, Marovitz's estate donated his papers to the Richard J. Daley Library at the University of Illinois at Chicago.
In 2003, Chicago–Kent College of Law began "The Honorable Abraham Lincoln Marovitz Public Interest Law Award", an award intended to recognize alumni who have demonstrated outstanding public interest. Recipients include the inaugural class of Jed Stone and Thu Tran, as well as Pablo Almaguer.