Preheat the broiler on high and position the oven rack about 6 inches from the heat source.
In a medium bowl, combine the drained tuna, mayonnaise, chopped red onion, chopped celery, lemon juice, salt, and black pepper. Mix well until all ingredients are evenly incorporated.
Spread the softened butter evenly on one side of each bread slice.
Place the bread slices butter-side down on a baking sheet.
Spread a thin layer of Dijon mustard on the top side of each bread slice.
Divide the tuna salad evenly and spread it over the mustard-coated side of each bread slice.
Top each open-faced sandwich with two slices of cheddar cheese, covering the tuna salad completely.
Place the baking sheet under the broiler and broil for 3 to 5 minutes, or until the cheese is melted, bubbly, and lightly browned. Watch carefully to prevent burning.
Remove the sandwiches from the oven and let them cool for 1 minute before serving.