1. Preheat oven to 450°.
2. Cut 4 (15 x 24–inch) pieces of parchment paper and fold in half, like a book. Draw a large heart half on each piece with the fold being the center of the heart. Cut out heart, and lay it open.
3. Lay 2 slices of lemon in the center of 1 side of each piece of parchment; top with 1 bay leaf, if desired, and 1 halibut fillet. Sprinkle fillets evenly with 1/2 teaspoon salt and 1/4 teaspoon pepper. Drizzle each fillet with 3/4 teaspoon olive oil. Fold other side of heart on top. Starting at the top of the heart, fold up both edges of parchment, overlapping the folds as you move along. Twist the end tip to secure tightly.
4. Place parchment packets on an ungreased baking sheet. Bake at 450° for 12 minutes. Remove from oven; let rest for five minutes.
5. Cook potatoes in boiling water 8 minutes or until potatoes are almost tender. Add green beans to pan; cook 4 minutes or until crisp-tender. Drain well; keep potatoes and green beans warm.
6. Working with one packet at a time, carefully open fish packets and pour liquid from packets into a large bowl. Add remaining 1 tablespoon olive oil, vinegar, juice, mustard, garlic, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper; stir well with a whisk. Add potatoes, beans, and onion to oil mixture; toss well to coat. Divide vegetable mixture evenly on each of 4 plates. Top each serving with 1 fillet.