Preheat oven to 375°. In a 6- to 8-quart pan, heat olive oil over medium heat. Add garlic and spinach and stir often until spinach is wilted, about 2 minutes. Remove spinach and chop. Return to pan. Add rice and stir to combine. Add 2 cups hot water and 1/2 teaspoon salt. Bring to a boil over high heat, then cover, lower heat, and simmer until rice is tender, about 15 minutes.
Stir in milk, dill, lemon juice, and pepper. Transfer mixture to an 8-inch square baking dish and spread level. Dollop sour cream, cover pan with foil, and bake until heated through, 10 to 15 minutes. Stir and serve.