Heat oven to 425° F. Cook the rice according to the package directions.
Meanwhile, toss the mushrooms, zucchini, and radishes with 2 tablespoons of the oil, 2 tablespoons of the lemon juice, ½ teaspoon salt, and ¼ teaspoon pepper. Roast on a baking sheet until tender and browned in spots, 20 to 25 minutes, tossing halfway through. Remove from oven and stir in the radish greens.
Whisk together the soy sauce, sesame seeds, and the remaining 3 tablespoons each of lemon juice and olive oil in a small bowl.
Serve the roasted vegetables and walnuts over the rice, drizzled with the dressing.