Stir yogurt, mayonnaise, celery, lemon zest, mustard, pepper and salt together in a medium bowl until well combined. Fold in chicken and onion until evenly coated.
Brush 1 side of each bread slice with melted butter (about ¾ teaspoon each); place bread, buttered-sides down, on a work surface. Spread ¼ cup chicken salad on each of 4 slices; top each with 2 tomato slices and 1 cheese slice. Top with the remaining 4 bread slices, buttered-sides up, pressing down slightly to flatten.
Heat a large cast-iron skillet over medium-low heat. Cook 2 sandwiches, covered with a lid slightly smaller than the skillet (so it presses on the sandwiches), until the cheese is melted and the bread is golden brown and crisp, 3 to 4 minutes per side. Transfer the sandwiches to a plate; loosely cover with foil to keep warm. Wipe the skillet clean; repeat the process with the remaining 2 sandwiches. Slice the sandwiches in half and serve immediately. Additional reporting by Carrie Myers, M.S. and Linda Frahm
