Arrange oven racks in top and bottom thirds of oven and preheat oven to 450°F.
Slice potatoes crosswise into 1/4-inch thick rounds, transfer to a bowl and toss with 1 Tbsp. olive oil. Arrange on a large, foil-lined baking sheet. Sprinkle with thyme, 1/2 tsp. salt and 1/4 tsp. pepper. Bake in bottom of oven for 30 minutes.
Meanwhile, combine fish and milk in a large bowl; turn fish to coat. Toss together cornmeal, chili powder, 1/2 tsp. salt and 1/4 tsp. pepper in a shallow bowl. Add 1 fish fillet and coat with cornmeal mixture. Transfer fillet to a large plate and repeat with remaining fillets.
Heat a large cast-iron skillet over medium heat. Add 2 Tbsp. oil, swirling to coat pan. Add fillets and cook until nicely crusted on bottom, about 2 minutes; carefully turn and then transfer skillet to top rack in oven. Cook until golden and firm when pressed in center, about 6 minutes. Serve with fresh lemon and vinegar.