Cover the lima beans with plenty of cold water and leave to soak overnight.
Drain well.
Bring a large pot of water to a boil, add the lima beans and return to a boil, then reduce the heat to medium and cook, partially covered, for 45- 60 minutes, or until the beans are tender but not mushy. Drain.
Preheat the oven to 350 F.
Heat the oil in a 3 quart heatproof casserole dish over medium heat. Add the onion, garlic, carrot and celery, and cook for 5 minutes, or until the onions is translucent.
Add the crushed tomato, paste and ½ cup water.
Bring to the boil, then reduce the heat and simmer for 3 minutes.
Add the lima beans and dill to the casserole dish, then season, to taste.
Bring back to the boil, then cover and bake for 50 minutes, or until the sauce is thick and the lima beans are soft. Serve hot or at room temperature, drizzled with the oil.