In a medium bowl, combine the drained tuna, mayonnaise, Dijon mustard, chopped celery, and diced red onion. Stir in the lemon juice, adding salt and pepper to taste. Mix until smooth and creamy.

Lay out eight slices of whole-grain bread and spread softened butter on one side of each slice.

Heat a skillet over medium heat until hot enough that the butter sizzles.

Place four slices of prepared bread, buttered side down, in the skillet. Layer with one slice of cheddar cheese, a scoop of the tuna mixture, tomato slices, and arugula.

Top with another slice of cheddar cheese and the remaining slices of bread, buttered side up.

Grill the sandwiches for 3–4 minutes on each side until golden brown and cheese is melted.

Remove from skillet, let cool for a minute, then cut each sandwich in half and serve warm.