Place lettuce in a 3-quart salad bowl. If desired, sprinkle with salt and pepper. Layer atop lettuce in the following order: mushrooms, broccoli, and/or peas, carrots, eggs, bacon, 1/2 cup of the cheese, and green onions. For dressing: In small bowl, combine the mayonnaise or salad dressing, lemon juice, and if desired, dillweed. Spread dressing over top of salad. Sprinkle with the remaining 1/4 cup cheese. Cover and chill for 2 to 24 hours. Before serving, toss to coat vegetables.