In a medium bowl, stir together the Greek yogurt, mayonnaise, celery, lemon zest, Dijon mustard, black pepper, and salt until smooth and well combined.
Fold in the shredded chicken and sliced red onion until the mixture is evenly coated.
Brush one side of each bread slice with melted butter. Place the bread slices buttered-side down on a clean work surface.
Spread about 1/4 cup of the Rotisserie Chicken Salad Melt filling onto 4 bread slices.
Top each with 2 tomato slices and 1 slice of American cheese.
Cover with the remaining bread slices, placing them buttered-side up. Press gently to flatten slightly.
Heat a large cast-iron skillet over medium-low heat.
Place 2 sandwiches in the skillet and cover with a lid slightly smaller than the pan so it gently presses the sandwiches.
Cook for 3 to 4 minutes per side, or until the bread is golden brown and crisp and the cheese is melted.
Transfer to a plate and loosely cover with foil to keep warm. Wipe the skillet clean and repeat with the remaining sandwiches.
Slice in half and serve right away.