In a mixing bowl, combine the drained tuna, light mayonnaise, chopped celery, chopped red onion, parsley, lemon juice, salt, and pepper. Mix well until everything is evenly combined.
Place the slices of whole wheat bread on a baking sheet and toast them under the broiler for about 1-2 minutes on each side, until they are lightly browned.
Remove the toasted bread slices from the oven and divide the tuna mixture evenly among them, spreading it out to cover each slice.
Top each slice of bread and tuna mixture with a slice of reduced-fat cheddar cheese.
Place the baking sheet back under the broiler and broil the tuna melts for 2-3 minutes, or until the cheese is melted and bubbly.
