Completely drain tuna and scoop into a small mixing bowl. Drain and rinse canned beans and add 1 cup to the tuna. (The remaining beans may be saved and used in scrambled eggs or even pureed and added to muffin batters.)
Chop tomato and parsley. Peel carrots and cut into sticks; core and slice apples.
Add tomato, parsley, 1-2 teaspoon of fresh lemon juice (more or less to taste), 1 teaspoon of lemon zest, oil, salt, and pepper to the tuna; mix well.
Toast muffins and scoop out tuna mixture onto each of 4 muffin halves. Add arugula and top with remaining muffin halves.
Serve with carrot sticks and apples slices on the side.