Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Arrange bread in a single layer on a baking sheet.
Toast bread lightly on both sides in preheated oven, about 1 minute per side.
Mix tuna, mayonnaise, lemon juice, lemon zest, and dill in a bowl. Spread tuna mixture evenly over each slice of bread. Arrange tomato slices over tuna mixture and top with Swiss cheese.
Return baking sheet to oven and broil until cheese is melted, 3 to 5 minutes more.