In a small saucepan, bring the sugar and water to a boil; remove from heat and cool.
Juice the lemons into a small bowl and strain. Add half of the sugar syrup to the lemon juice, adding more sugar syrup until the desired balance of sweetness and tartness is reached; cool to room temperature.
Season flounder fillets with salt and pepper then drizzle with olive oil. Place a large skillet over medium-high heat; add fish then lower the heat to medium.
Cook until well-browned on one side (about 3 minutes) then turn and cook for 1 minute. Serve flounder topped with lemon sauce.