In a bowl, combine the drained tuna, mayonnaise, chopped red onion, lemon juice, salt, and pepper. Stir until the ingredients are well mixed. Adjust mayo or seasoning to taste.
Butter one side of each slice of bread.
On the unbuttered side of two slices of bread, place a slice of cheddar cheese. Add a layer of the tuna mixture on top of the cheese. Add any other ingredients you'd like, such as tomato or avocado slices.
Finally, cover with the remaining slices of bread, ensuring the buttered sides face outward.
Heat a skillet over medium-low. Cook the sandwiches 2-5 minutes per side, pressing gently for even toasting.
When both sides are golden and the cheese is melted, remove from the skillet and serve immediately.