From fresh fish, cut off heads and gut. Wash the fish with cold water and pat dry with a paper towel. Sprinkle with salt, pepper, and lemon juice. Coat the fish in flour on both sides. Dredge off excess flour.
Place two lemon halves in a large dry skillet and grill flesh side down until golden. Remove to the side. Pour in and heat a small amount of oil. Then add 2 tablespoons of butter. Melt and heat slowly, over medium heat so the butter doesn't burn. Place the flounder on the darker side and fry until lightly browned. Then fry on the other side. Remove to a plate nearby.
Add 1 more tablespoon of butter to the pan and add the sundried tomatoes cut into strips and the capers. Pour in the cream and add almost all the parsley. Stew while stirring for 2 minutes. Put the fish into the sauce for one minute.
Serve the flounder immediately hot with a slice of fresh crusty bread.