Preheat oven to 400 degrees F.
In a small bowl, stir together the ricotta cheese, 1/4 cup of the Parmesan cheese, minced garlic, fresh lemon juice, crushed red pepper, salt and black pepper, to taste. Set aside.
In a small skillet, heat the olive oil over medium high heat. Add the sliced Brussels sprouts and sliced red onion. Cook for 3 minutes, just until Brussels sprouts and red onions are softened. Set aside.
Place the flatbread on a large baking sheet. Spread the ricotta cheese mixture evenly over the flatbread with a spatula. Top evenly with shredded mozzarella cheese, remaining Parmesan cheese, Brussels sprouts, and onions.
Place the flatbread in the oven and bake for 10-12 minutes or until cheese is melted and the flatbread is golden brown. Remove from the oven and squeeze a little fresh lemon juice over the top. Sprinkle with extra Parmesan cheese, if desired. Cut into slices and serve immediately.