Put the oil in a large skillet or flameproof casserole with a lid over medium heat. A minute later, add the onion, along with some salt and pepper, and cook, stirring occasionally, until it wilts, about 5 minutes. Add the beans, about half the dill, and 1 cup water. Lower the heat, cover, and adjust the heat so the mixture simmers steadily. Cook until the beans are quite tender, 20 to 30 minutes.
Uncover and raise the heat so any excess liquid boils away. Add the lemon juice, then stir; taste and adjust the seasoning. Turn off the heat, stir in the yogurt, garnish with the remaining dill, and serve.