In a medium bowl, combine drained tuna, mayonnaise, celery, red onion, and lemon juice. Mix well and season with salt and pepper.
Butter one side of each bread slice. Place 4 slices butter-side down on your work surface.
On each unbuttered side, place one slice of cheese, then divide the tuna mixture evenly among the 4 slices.
Top tuna with another slice of cheese, then place remaining bread slices on top, butter-side up.
Heat a large skillet over medium heat. Cook sandwiches for 3-4 minutes per side until bread is golden brown and cheese is fully melted.
Let cool for 1 minute before slicing. Serve with pickles or chips on the side!