In a medium bowl, combine the drained tuna, mayonnaise, chopped celery, chopped red onion, and lemon juice. Mix well.
Season the tuna salad with salt and black pepper to taste. Stir to combine.
Butter one side of each slice of bread.
Place two slices of bread, butter-side down, in a non-stick skillet or on a griddle over medium heat. Top each with a slice of cheddar cheese.
Spoon half of the tuna salad mixture onto the cheese on each sandwich.
Top with the remaining two slices of bread, butter-side up.
Grill for 4-5 minutes per side, or until the bread is golden brown and the cheese is melted.
Remove from skillet, slice in half, and serve immediately.
Notes
You can add other ingredients to the tuna salad such as dill pickles, relish, or hard-boiled eggs. Experiment with different types of cheese and bread for variety!