Place quinoa in a bowl; pour in enough water to cover. Soak for 30 minutes. Drain and rinse several times.
Bring quinoa, water, olive oil, and 1 teaspoon salt to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until quinoa is tender and the water has been absorbed, about 20 minutes.
Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch square baking dish.
Place a steamer insert into a saucepan and fill with water to just below the bottom of the steamer. Bring water to a boil. Add broccoli, cover, and steam until tender, 2 to 4 minutes.
Stir broccoli, cream of mushroom soup, Cheddar cheese, 1/2 cup French-fried onions, sour cream, and lemon pepper into cooked quinoa; season with salt and black pepper to taste. Spoon quinoa mixture into the prepared baking dish.
Bake in the preheated oven until heated through, 10 minutes. Sprinkle with 1/2 cup French-fried onions and bake until topping is lightly browned, about 5 more minutes.
