Set up your grill or smoker for indirect grilling and preheat to 225° degrees. Brush the grill grate clean and oil it well.
In a small bowl, combine the barbecue rub and the smoked paprika. In another bowl, combine the barbecue sauce with the honey and lemon juice. Set aside.
Place the ribs on a rimmed sheet pan. (For easier cleanup, line the pan with Reynolds Wrap® Heavy Duty Foil.) If your butcher has not already done so, remove the tough papery membrane on the back of the bones and discard. Using a sharp paring knife, make shallow cuts on either side of and close to each bone on the back of the ribs. This extra step makes deboning the ribs easier once they are cooked.
Season the ribs on both sides with the barbecue rub; don’t forget the ends.
Place 3/4 cup of wood chips on each pile of coals or in the smoker box of your gas grill. Lacking a smoker box, place a foil smoking pouch (see Notes below) over one of the burners on your gas grill (under the grill grate).
Place the ribs directly on the grill grate, meat side up, away from direct heat. Smoke the ribs, lid down, for 2 hours, replenishing the fuel and wood chips as needed.
Transfer the ribs, meat side up, to the prepared sheet of foil, long sides parallel to each other. Turn the sides and ends of the foil up slightly. Pour the lemon-lime soda around the bottom of the rack. Bring the ends of the foil together and fold twice to make a tight seal. Repeat with the sides. (If using Reynolds Wrap® Heavy Duty 18” Extra-Wide Foil, bring the long sides over the ribs first, fold, then fold the ends)
Return the foiled ribs to the grill, seam side up. Replace the lid and cook the ribs for an additional 2 to 2 1/2 hours, replenishing the fuel as needed. (You do not need smoking chips once the ribs are foiled)
Transfer the ribs to a rimmed sheet pan or cutting board. Carefully open the foil package, avoiding any escaping steam. Discard the foil and any accumulated juices. Brush the ribs on both sides with the reserved barbecue sauce.
Return the ribs to the grill, meat side up, and continue to cook for 30 minutes to 1 hour, or until the sauce sets and the ribs are very tender. The meat will have shrunk from the ends of the bones by 1/2-inch; a toothpick inserted between the bones near the center of the rack should pierce the meat easily.
Using a spatula and tongs, carefully transfer the ribs, bone side up, to a cutting board. (Try to keep the rack from flexing and tearing by supporting it in the middle with the spatula.) Carefully remove the bones. They should release easily with minimal help from a paring knife.
Arrange the now-boneless ribs meat side up on the bottom portion of the bread. Brush the top of the ribs with additional barbecue sauce, if desired. Top with pickle chips and sliced onions. Drizzle lightly with barbecue sauce. To serve, slice the sandwich into 2 or 3 equal portions using a serrated knife.
If using 12-inch-wide Reynolds Wrap® Heavy Duty Foil, tear off a piece that is twice as long as the rack of ribs plus 4 inches. If using Reynolds Wrap® Heavy Duty 18” Extra-Wide Foil, tear off a piece that is 4 inches longer than the rack of ribs.
If you are cooking the ribs on a gas grill, place the soaked wood chips in the grill’s smoker box. Or make a pouch out of Reynolds Wrap® Heavy Duty Foil and fill it with soaked wood chips. Fold the edges to completely enclose the chips. Poke holes in the pouch so the smoke can escape. Place the pouch over one of the burners or on the grill grate. Replace as needed during the first 2 hours of the cook.