Whisk together orange juice, lemonade, onion, olive oil, garlic, oregano, and lime juice in a medium bowl to make the marinade.

Trim excess fat from the pork loin.

Place the pork loin in a resealable plastic bag and pour in the marinade.

Seal the bag tightly, removing as much air as possible.

Refrigerate the pork for 4 to 6 hours, turning occasionally to distribute the marinade.

Remove the pork from the bag and discard the marinade.

Let the pork stand at room temperature for 20 to 30 minutes.

Pat the pork dry with paper towels and season with salt and pepper.

Sear the pork over direct medium heat for about 10 minutes, turning once, until well marked.

Continue grilling over indirect medium heat until the internal temperature reaches 155°F, about 35 to 45 minutes.

Transfer the pork to a carving board and loosely cover with foil.

Let the pork rest for about 10 minutes.

Slice the pork crosswise as thinly as possible.

Split the French rolls and spread the inside of each roll with 1 tablespoon of softened butter.

Grill the rolls, cut side down, over direct medium heat until toasted, about 30 seconds.

Layer each roll with Swiss cheese, ham, pickle slices, and sliced pork loin.

Flatten the sandwiches on a cutting board with the palm of your hand.

Grill the sandwiches over direct medium heat for 30 seconds.

Turn the sandwiches and press down firmly with a metal spatula, grilling for 30 seconds more.

Serve warm or at room temperature.