If using fresh greens, discard any tough stems and chop the leaves. Rinse and shake gently to remove most but not all of the water. Place 2 tablespoons of the oil in a large stockpot with the garlic and cook over medium-high heat. As soon as the garlic begins to brown, add the greens and toss. Add 1/2 teaspoon of the salt. Cover immediately and cook over medium heat, stirring occasionally, for 10 minutes or until very tender. (If using frozen spinach, press out the liquid, then sauté the spinach in 2 tablespoons of the oil and the garlic for about 5 minutes.) Remove from heat and set aside to cool.
Meanwhile, in a medium saucepan over medium heat, combine the remaining olive oil, the flour, and the remaining salt. Cook, whisking constantly, for about 3 minutes. Add the milk and increase heat to medium-high. Cook, stirring constantly, until the sauce thickens and boils, about 10 minutes. Stir in all but 1/2 cup of the grated cheese.
Heat oven to 350º F.
Coat a 13-by-9-inch baking pan with cooking spray. Blend the ricotta, eggs, lemon zest, and nutmeg into the greens. Spread about 1/2 cup of the cheese sauce in the bottom of the baking pan. Place 3 sheets of pasta on top. Spread on 1/4 of the spinach filling and 1/2 cup sauce, then another 3 sheets of pasta. Make 3 more layers. End with the pasta and sauce, and sprinkle with the remaining cheese. Cover with foil and bake 45 minutes. Remove the foil and cook 15 minutes more or until golden.
Let stand 10 minutes before serving. (Can be made up to 1 day ahead. Cover and refrigerate. Reheat in a 325º F oven for 20 minutes or until a knife inserted in the center comes out hot.)