Boil and cool the eggs: Place eggs in a pot, cover with cold water, bring to a boil, turn off heat, cover, and let sit for 10-12 minutes. Transfer to cold water to cool.
Drain and prep the tuna: Drain tuna well, press out extra liquid, and flake into a mixing bowl.
Chop the mix-ins: Chop eggs, celery, and red onion finely. Keep pickle or relish modest if using.
Mix the filling: Add eggs, mayonnaise, Dijon mustard, lemon juice, celery, onion, and pickle to tuna. Season with salt and pepper, fold gently until creamy and mixed. Taste and adjust seasoning if needed.
Prep the bread and build the sandwich: Toast bread lightly if desired. Spread filling on bread, add lettuce and tomato if using, and serve.