Heat grill to medium. In a small bowl, combine butter, dill, and garlic; season with salt and pepper. Set aside.
Fold four 14-inch squares of heavy-duty aluminum foil in half, forming 4 rectangles. Assemble packets: On one half of each of four folded pieces of heavy-duty foil, dividing ingredients evenly, arrange potatoes in a single layer; top with cod, then shrimp. Place 2 pieces of corn on the side. Season with salt and pepper. Add a dollop of the butter mixture and two lemon slices. Fold foil over ingredients, and crimp edges tightly to seal.
Place packets on grill, with potato layer on the bottom. Cook, rotating (but not flipping) packets occasionally, until fish is just cooked through and potatoes are tender, 12 to 14 minutes.
Remove from grill. Slit packets open, and transfer contents to serving bowls. Garnish with dill sprigs; serve with rolls.