Drain the tofu and press it lightly with paper towels or a clean kitchen towel for about 10 to 15 minutes. Transfer the tofu to a medium bowl and break it up with your hands or a fork. Mash part of it until it looks crumbly and soft, but leave some small chunks so the texture feels more like classic egg salad and less like spreadable dip.
In a small bowl, stir together the vegan mayo, Dijon mustard, lemon juice, turmeric, black pepper, regular salt, and black salt. Mix it well so the color looks even and the seasonings get fully distributed before they hit the tofu. Taste the dressing before adding it to the tofu, because this is your easiest chance to adjust the balance.
Add the chopped celery, red onion, dill, and pickle or relish to the bowl with the tofu. Pour the dressing over everything and fold it together gently so the tofu keeps some texture instead of getting smashed into oblivion. Let the mixture sit for 5 to 10 minutes if you have the time.
Taste the filling again and make your final adjustments. Spread the filling onto four slices of bread and top with lettuce or tomato if you like. Add the remaining bread slices, press gently, and slice each sandwich in half so it actually feels like lunch and not just a pile of filling trapped between two carb blankets.
Serve the sandwiches right away if you want the best contrast between creamy filling and fresh bread. If you are packing them for later, place lettuce between the filling and bread to create a little barrier.