Preheat oven to 500°.
Snap off tough ends of asparagus; cut spears into thirds.
Combine asparagus, onion, and mushrooms on a foil-lined baking sheet. Drizzle with oil, and sprinkle with 1/4 teaspoon salt; toss gently. Bake at 500° for 8 minutes or until roasted.
Combine 3 cups water and remaining 1/4 teaspoon salt in a large saucepan; bring to a boil.
Stir cornmeal into remaining cup of water. Add cornmeal mixture to boiling water, stirring constantly. Cook 4 to 5 minutes or until thickened, stirring occasionally. Stir in cheese.
Sprinkle vegetable mixture with chives and lemon juice; toss gently. Serve over polenta.