Thaw tuna, if frozen. Brush tuna generously with oil; sprinkle with salt and pepper. Cover and refrigerate for 2 hours.
Combine the water and half of the lemon juice in a medium bowl. Add onion; soak for 15 minutes. Drain.
Grill tuna on the oiled rack of an uncovered grill directly over medium heat for 4 to 6 minutes or until just opaque in the center, turning once. Break into chunks with two forks.
Stir together mayonnaise, relish, lemon peel, the remaining lemon juice, the garlic, and mustard in a medium bowl. Add tuna; stir gently to combine. Spoon mixture onto bottoms of rolls. Top with onions. If desired, add sliced eggs, pickle slices, tomato slices, and a few sprigs of dill. Top with remaining roll halves. Makes 4 servings.