Drain the tuna well and place it into a medium bowl. Using a fork, break up the chunk.
Into the same bowl with the tuna, add the mayonnaise, onion, lemon juice, salt, pepper, celery, green onion, and green onion and mix until combined, set aside.
Heat a skillet to medium-low heat.
Spread butter on one slice of bread. Place this piece of bread, butter side down, into the skillet. Add about ½ cup of the tuna mixture and spread it to the edges of the bread.
Add 2 slices of the tomato and 1 slice of the cheese.
Butter one side of another piece of bread and place this piece of bread (butter side up) on top of the cheese
Carefully flip the sandwich with a spatula to grill both sides.
Cook the sandwich in the skillet at medium-low heat until the cheese is melted, and the bread is toasted, and everything is heated through.
Remove from the pan and serve immediately.