In a mixing bowl, combine the drained tuna, mayonnaise, finely diced celery, minced parsley, sweet pickle relish, and freshly squeezed lemon juice. Stir until all ingredients are well incorporated and the mixture is creamy. Season with salt and pepper to taste.
Take two slices of sourdough bread and generously spread the tuna filling on one side of each slice. Top the filling with a sprinkle of shredded sharp cheddar cheese for that melty goodness. Place the other two slices of bread on top, creating two sandwiches.
Heat a skillet or griddle over medium heat. Once hot, add a little butter or olive oil to the pan. Carefully place the sandwiches on the skillet and cook for about 3-4 minutes, or until the bottom is golden brown. Flip the sandwiches and cook for an additional 3-4 minutes on the other side, making sure the cheese is melting and the bread is perfectly toasted.
Once the Deluxe Tuna Melts are golden brown and the cheese has melted, remove them from the skillet. Allow them to cool for a minute before slicing in half. Serve warm with your favorite sides, such as a crisp salad or potato chips, and enjoy!