Bring 1 cup water to a simmer in a saucepan over medium-high heat. Add the lima beans and cook until softened, 8 minutes. Stir in the spinach until wilted.
Transfer the vegetables and liquid to a food processor along with the tahini, cilantro, 1/2 cup water, the dill, olive oil, lemon zest and juice and garlic; season with salt and pepper. Puree until mostly smooth, adding more water if needed.
Transfer the dip to a bowl and drizzle with olive oil. Top with feta and dill. Serve with crudités.