Cook lasagne according to package directions; drain.
Preheat oven to 350ºF. Warm oil in a large saucepan over low heat.
Add onion, garlic and eggplant. Cover and let vegetables cook until very soft, about 10 minutes. Meanwhile, stir together the Ricotta, Feta and yogurt.
When vegetables are done, stir in tomato sauce. Remove from heat and set aside 1 cup of eggplant mixture.
In a 9 × 13 × 2-inch baking dish, spread a little of the eggplant mixture over the bottom and cover with 3 pieces of lasagne. Spoon some of the Ricotta over the lasagne. Continue to layer with eggplant mixture, lasagne, and Ricotta. Place a layer of lasagne on top. Spread the reserved eggplant over lasagne and sprinkle with Parmesan. Bake uncovered for 45 minutes, until cheese is brown.