Heat the oven to 400°F. If using the broiler for the final finish, position the rack appropriately and plan to watch the melts closely.

In a medium bowl, combine the thoroughly drained and flaked tuna with mayonnaise, celery, onion, sweet pickle relish, Dijon mustard, lemon juice, salt, and black pepper. Stir until the ingredients are evenly blended but still retain some texture.

Arrange the eight split English muffin halves cut-side up on a baking sheet. Toast them for 3–4 minutes if you prefer a crisper base before adding the tuna mixture.

Divide the tuna mixture evenly among the eight muffin halves, spreading it close to the edges without pressing it down too firmly. This creates a generous layer that warms quickly and supports the cheese.

Place one cheddar slice on each filled muffin half. Keep the cheese centered so it melts over the tuna without sliding too far onto the baking sheet.

Bake for 6–8 minutes, until the tuna filling is hot and the cheddar has melted. For bubbling, lightly browned cheese, broil the assembled melts for 2–3 minutes instead, watching continuously.

Serve the tuna melts immediately while the muffin edges are crisp and the cheese is soft. Use a spatula to transfer them carefully from the baking sheet to plates.