Majeiritsa (Easter Lamb Soup)

2 tablespoons olive oil
2 onions, finely chopped, or 6 to 7 green onions, finely chopped
8 cups chicken broth
1 pound boneless lamb, trimmed of excess fat and cut
    into 1/4- to 1/2-inch pieces
1 1/2 cups chopped fresh Italian parsley
1/2 cup chopped fresh dill
1/3 cup long-grain rice
4 large egg yolks, at room temperature
1/2 cup fresh lemon juice (about 2 lemons)
Salt and freshly ground pepper to taste

In a large stockpot over medium heat, add the olive oil. Saut