In a large saucepan, heat oil over medium-high. Add onion, carrots, celery, and bay leaf. Cook, stirring, until vegetables are softened, 5 to 7 minutes. Add garlic and curry powder and cook until fragrant, about 1 minute more.
Add 7 cups of water and lentils. Bring to a boil, reduce to a simmer, cover, and cook 10 minutes. Add potatoes and continue to cook, covered, until lentils and potato are just tender, about 15 minutes.
Add green beans and tomatoes with juice. Cook until warmed through, 2 to 4 minutes. Remove bay leaf. Add cilantro; season with salt and pepper. Serve with yogurt.