In a large saucepan bring 2 inches of water to boiling. Add potatoes and fresh green beans, if using. Cover and simmer 10 minutes or just until tender. If using frozen beans, add to potatoes the last 5 minutes of cooking. Remove beans with a slotted spoon. Rise beans with cold water; drain. Drain potatoes. Cover and chill beans and potatoes separately for 2 to 24 hours.
Meanwhile, for dressing, in a screw-top jar combine lemon juice, oil, mustard, dillweed, water, salt, and pepper. Cover and shake well to blend. Chill for 2 to 24 hours.
To serve, place lettuce leaves on a platter. Arrange potatoes, beans, tuna, tomatoes, onion, and eggs atop lettuce. Shake dressing and drizzle over salad. Makes 4 servings.