In a large nonstick skillet, arrange the pork belly slices in a single layer. Season with salt and pepper and cook over moderate heat, turning once, until browned and crisp, about 8 minutes. Pour off all but 2 tablespoons of the fat and add the spinach to the pork in the skillet. Season with salt and pepper and stir until the spinach is wilted. Crack the eggs into the skillet and cook for 2 minutes. Using a wide spatula, gently turn the eggs with the pork and spinach, trying not to scramble the eggs. Cook just until the whites are set but the yolks are runny, about 2 minutes. Sprinkle with the lime juice.