Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 20 to 25 minutes.
Heat oil in a saucepan over medium-high heat. Saute onion until tender, about 5 minutes. Add the cooked rice and spinach; cook and stir until spinach wilts, 3 to 5 minutes. Add lemon juice, zest, feta cheese, and dill. Remove from heat. Season with salt and pepper.