It's not a Nazi plane, but rather a French plane that would transport Nazis and gold ingots, according to its commander. Some relevant in-depth piece of news is in here. It's in Spanish obviously. The plane was nicknamed Lioner de Marmier. The lake is called Laguna Negra, in the department of Rocha.

If you're into 4AM History Channel kind of shows, Hunting Hitler delves into the story. They find bits and pieces of a plane in the lake. After reading the story, I don't know if the entire plane is down there anymore.