Mix the tuna salad: In a bowl, combine drained tuna, mayonnaise, Dijon, red onion, celery, relish, lemon juice, salt, and pepper. Stir until evenly mixed.
Adjust mayo and seasoning to your taste.
Prep the bread: Spread a thin layer of butter or mayonnaise on one side of each bread slice. This helps with browning and flavor.
Assemble the melts: Place two slices of bread, buttered side down, on a plate. Add a slice of cheese to each, spoon a generous layer of tuna salad on top, then add another slice of cheese.
Cap with the remaining bread, buttered side facing out.
Preheat the air fryer: Set it to 370–380°F (188–193°C) for 2–3 minutes. A short preheat helps the bread crisp right away.
Air fry: Place the sandwiches in the basket in a single layer. If your basket has wide grates, consider lining with perforated parchment to prevent sticking.
Cook for 4–6 minutes, then flip carefully and cook another 3–5 minutes, until the bread is golden and the cheese is melted.
Watch for doneness: Every air fryer is a bit different. Look for deep golden edges and melted cheese peeking through. If the bread is browning too quickly, lower the temperature to 360°F (182°C) and continue until the cheese melts.
Rest and slice: Let the sandwiches sit for 1–2 minutes to set, then slice diagonally.
Serve hot.