Try to purchase cod fillets that are similar in size so that they cook at the same rate. If the fillets are much thinner than 1 inch, simply fold them over to make them thicker. Halibut and haddock are good substitutes for the cod.
Adjust oven rack to lower-middle position and heat oven to 425 degrees. Brush 13 by 9-inch baking dish with 1 tablespoon oil.
Toss potatoes with remaining 1 tablespoon oil and garlic and season with salt and pepper. Shingle potatoes into baking dish in 2 rectangular piles measuring 4 by 6 inches. Roast potatoes until spotty brown and just tender, 30 to 35 minutes, rotating dish halfway through roasting.
Pat cod dry with paper towels and season with salt and pepper. Carefully place 1 fillet, skinned side down, on top of each potato pile. Top fillets with butter pieces, thyme sprigs, and lemon slices. Roast cod and potatoes until fish flakes apart when gently prodded with paring knife and registers 140 degrees, about 15 minutes.
Slide spatula underneath potatoes and fillets and gently transfer to individual plates. Serve.
