1. Bring the sugar and water to a boil. Remove from the heat and cool.
2. Juice the lemons and strain. Add half of the sugar syrup to the lemon juice. Add more sugar syrup until a pleasant balance of sweetness and tartness is reached. Cool to room temperature.
For the flounder:
1. Season the flounder fillets with salt and pepper, then drizzle with olive oil.
2. Place a sauté pan large enough to accommodate all the fillets over medium-high heat. Add the flounder and lower the heat to medium. Cook until well-browned on one side, about 3 minutes. Turn the fillets over and cook 1 more minute.
3. Serve the flounder topped with the lemon sauce.