Melt 1/4 cup of butter in a large skillet over medium heat. Add the onion, and cook for about 5 minutes, until tender. Add the chopped livers and ground lamb. Cook, stirring to crumble, until evenly browned. Stir in the rice, cinnamon, mint and tomato paste. Mix in 1 cup of the water, and season with salt and pepper. Cook over low heat for 10 minutes, stirring constantly.