Preheat the oven to 200°F. For the sauce, in a medium bowl, stir the yogurt, lemon juice, dill, onion, pickle relish, Dijon, capers, and garlic; season with salt and pepper.
For the fish, sprinkle the fillets with the granulated garlic; season with salt and pepper. Squeeze the juice from the ½ lemon on top of the fish. In a shallow bowl, whisk the flour and cornstarch. In a second shallow bowl, whisk the eggs and milk; season with salt.
In a large nonstick skillet, heat the oil, one turn of the pan, over medium-high. Add half the butter. Dredge 2 fillets in the flour; coat with the egg. When the butter stops foaming, add the fish. Cook, turning occasionally, until opaque in the centers, 6 to 7 minutes. Transfer to a baking sheet and keep warm in the oven. Repeat with the remaining butter, fish, flour, and eggs.
Serve with lemon wedges. Top the toast with some shredded lettuce and the fish — and lots of tartar sauce.