Lasry was born in Marrakech to a family of Moroccan Jews. When he was seven years old, he and his family immigrated to the U.S. His Father, Moise, was a computer programmer and his mother, Elise, was a schoolteacher. Lasry grew up in West Hartford, Connecticut and received a B.A. in history from Clark University in 1981 and a J.D. from New York Law School in 1984. While in law school, he worked as a clerk for the Chief Bankruptcy Judge of the Southern District of New York, Edward Ryan.

In 1989, Lasry and his sister founded the firm Amroc Investments with $100 million in seed money from various Investors. Amroc purchased both trade claims and bank debt held by vendors of bankrupt and/or distressed companies. In 1995, Lasry and Gardner invested $7 million of their own capital and founded the Avenue Capital Group, which initially focused on distressed debt and special situations primarily in the United States. The partners successfully expanded the firm's investment focus to Europe and Asia. The two went on to build their hedge fund, which had as much as $11 billion in assets under management.

Lasry served as a Director of the 92nd Street Y and the Big Apple Circus and was a trustee of the Mount Sinai Hospital (Manhattan). He is a prominent donor to Democratic Party causes.

In 2004, Lasry and his wife contributed support to the University of Pennsylvania and co-chaired the Penn Parent Leadership Committee. In 2005 they donated $5 million to Clark University for the construction of the “Cathy '83 and Marc '81 Lasry Center for Bioscience”.

In 2013, Lasry was considered for the position of U.S. ambassador to France, but declined consideration for Business reasons. In 2014 Forbes listed Lasry as one of the 25 highest-earning hedge fund managers in 2013, with total earnings of $280 million.

In April 2014, Lasry became co-owner of the NBA's Milwaukee Bucks after purchasing the team from Herb Kohl for $550 million. Following the 2016 U.S. election, Lasry and the Milwaukee Bucks became one of three NBA teams to openly state they would not be staying at Trump branded hotels when on the road.

In January 2016 Lasry participated in "Portfolios with Purpose," an annual stock selection contest in which participants pick portfolios on behalf of their favorite charities.