In a medium bowl combine lemon juice, vinegar, mustard, salt, and the ¼ teaspoon pepper. Add the oil and whisk until fully blended. Set aside.
Wash the lettuce leaves, dry well and keep whole or tear into large pieces. Arrange in blossom or flower shape on serving platter, or toss in large salad bowl. Add the radicchio, green onions, radishes and tomatoes; either placing over butter lettuce on serving platter or tossing with lettuce in bowl.
Drizzle salad dressing over salad if serving on platter and sprinkle with capers and top with shaved Parmesan. If using salad bowl, toss dressing, capers, and cheese before serving.