Lyonne was born Natasha Braunstein in New York City, the daughter of Yvette Lyonne, a product licensing consultant, and Aaron Braunstein, a native of Brooklyn who worked as a boxing promoter. Lyonne grew up in an Orthodox Jewish household and lived in Israel with her family during her childhood; her maternal grandparents were Holocaust survivors. When her parents divorced, Lyonne moved back to New York and lived with her mother and older brother Adam in a one-bedroom apartment.

Lyonne attended several schools. She first attended a private Jewish school at Ramaz in Manhattan. Her mother then moved to Miami, where Lyonne attended and graduated from Miami Country Day School.