Blanch basil in a 1-quart saucepan of boiling water 15 seconds, then transfer with a slotted spoon to a bowl of ice and cold water to stop cooking. Squeeze excess liquid from basil and purée in a blender with garlic, salt, and 3 tablespoons oil.
Preheat broiler. Line rack of a small broiler pan with foil, then oil foil.
Stir together brown sugar and vinegar until sugar is dissolved, then overlap tomato slices on a large plate and drizzle with vinegar mixture. Season with salt.
Put fish, skin side down, on pan, then season with salt and pepper and drizzle with remaining 1/2 tablespoon oil. Broil fish about 3 inches from heat (without turning) until just cooked through, 6 to 8 minutes.
Put fish on top of tomatoes and spoon basil sauce on top. Serve with lemon.
