Zest and juice the lemon over a small bowl. Add the onion and salt then squeeze the onion slices with your fingers to break the cell walls and distribute the salt and lemon juice. Set aside to pickle for at least 10 minutes until bright fuscia and soft (reserve the pickle juice for serving).
Warm the olive oil over medium heat in a large skillet. Pat the fillets dry with paper towel then season both sides with salt and pepper. Place the fillets in the skillet, skin side down. Cook until the flesh is half-cooked and the skin is crisp, about 6 minutes. Turn fillets and immediately turn the heat off. Surround the fillets with the olives, capers, and parsley. The residual heat will continue to cook the fish until opaque and flaky, about 4 minutes.
Serve the fillets with the olive parsley sauce from the pan and top with the pickled onion plus the lemon juice in the bottom of the bowl.
How to Buy Fish
I love when fish is sold whole because then you can really see for yourself how fresh it is. Really fresh fish will have bright and clear eyes and the flesh will be firm to the touch. Fresh fish should smell pleasant, like the ocean. You can fillet the fish yourself or ask the fish monger to do it for you.*Sea bream, black sea bass, tilefish, or cod would all work well in this recipe.