In a medium mixing bowl, flake the drained tuna with a fork. Add the mayonnaise, finely diced celery, minced red onion, dill pickle relish, Dijon mustard, and fresh lemon juice. Mix gently until all ingredients are well combined. Season with salt and black pepper to taste.

Lay the four slices of bread on a clean surface. Generously butter one side of each slice. This will be the side that browns in the skillet.

Flip two of the bread slices so the unbuttered side is facing up. Evenly spread half of the tuna salad mixture onto each of these unbuttered sides. Place a slice of cheese (or half of the shredded cheese) on top of the tuna salad on each sandwich. Top with the remaining two slices of bread, buttered-side up.

Heat a large skillet or frying pan over medium-low heat. Once warm, carefully place the assembled tuna melts into the pan.

Cook for 4-6 minutes per side, or until the bread is golden brown and crispy, and the cheese is completely melted and gooey. You may need to press down gently with a spatula occasionally to ensure even contact with the pan. If the bread browns too quickly, reduce the heat.

Once cooked, carefully remove the tuna melts from the skillet. Slice them in half diagonally and serve immediately with your favorite side, such as a pickle spear, chips, or a simple green salad.