"Fish" is intentionally vague here. I've pan-seared cod, but the preparation could be poached, grilled, roasted, skillet-grilled (which I appreciated even more after this recent go at pan-frying), etc. And the fish could be anything you like—this sauce is very versatile. With that in mind, too, the sauce could work with chicken, steak, polenta, eggplant, cauliflower, etc.—it's versatile.
Combine the tomatoes, olives, and capers in a bowl. Pat the fish dry. Season well with salt and pepper on both sides.
Set a large sauté pan over high heat. Add a thin layer of oil. When it shimmers, carefully lower in the fish fillets. Reduce the heat to medium. Let the fish cook for two to three minutes undisturbed. Using a spatula, carefully nudge the fish to release it from the pan, then flip it. Cook for 1 to 2 minutes more, then transfer it to a serving plate.
Wipe out the pan. Add the tablespoon of olive oil and the minced garlic. The garlic should sizzle nearly immediately. Cook, shaking the pan for about 30 seconds, then add the tomato mixture. Cook for another 30 seconds, shaking the pan every so often. Juice the lemon into the pan. Add the parsley and stir to coat. Cook for another 30 seconds or until the tomatoes have softened ever so slightly. Remove the pan from the heat, spoon the sauce over the fish, and serve with more lemon on the side.