Preheat oven to 350 degrees.
In a small bowl, mash avocado with a fork. Add the tuna, lime juice, salt and pepper. Stir until well combined.
Place the English muffin halves onto an ungreased baking sheet. Evenly portion the tuna and avocado mixture onto each English muffin half. Top each with a tomato slice and cheese.
Bake for 10 minutes, then broil for 2 - 3 minutes until the cheese is golden and the edges of the muffins are toasted.