Rinse and pat the fish dry. Grate about 2 teaspoons of zest from the lemon and set aside, then cut the lemon in half. Squeeze the juice from half of the lemon over the fish and sprinkle the fish with salt. Cut the remaining lemon half into wedges and reserve.
Fill a medium saucepan three-quarters full with water, season with salt and bring to a boil. Add the potatoes and cook until tender, 10 to 12 minutes.
Meanwhile, place a large nonstick skillet over medium-high heat. Add 2 tablespoons of the EVOO, 2 turns of the pan, then add the cod. Cook the fish, breaking it up into small pieces with a spatula. When the fish is cooked through and the liquids have evaporated, about 6 minutes, transfer to a large bowl and let cool. Rinse and dry the skillet.
Drain the potatoes well and transfer to the bowl with the fish. Using a potato masher or a fork, mash the fish and potatoes together until a thick mixture forms. Add the dill, cayenne, salt and black pepper to taste and the reserved lemon zest and stir until combined. Form into 8 thick 3-inch-wide patties.
Heat 2 tablespoons of the EVOO, 2 turns of the pan, in a small nonstick skillet over medium-high heat. When the olive oil ripples, add the garlic and the Cubanelle and bell peppers and fry for 5 minutes.
Heat the remaining 2 tablespoons of EVOO, 2 turns of the pan, in the same skillet you cooked the fish in. When the oil ripples, add 4 of the fish cakes and cook until deeply golden all over, 3 to 4 minutes on each side. Repeat with the remaining fish cakes, using more olive oil if needed.
Add the sweet pickled and hot peppers and the parsley to the fried peppers and garlic. Season the relish to taste with salt and pepper and remove from the heat. Serve the cod cakes, 2 per person, with mounds of the pepper relish on top and the lemon wedges on the side to squeeze over the cod cakes.