Light a grill or preheat the oven to 500°. Using a small, sharp knife, peel the lemon, removing all the bitter white pith. Cut the lemon into 1/4-inch dice, discarding the seeds. Transfer the diced lemon to a medium bowl and add the tomatoes, cucumber, shallot, thyme and chives. Stir in the 1/4 cup of olive oil and season with salt and pepper.
Lay two 20-inch-square sheets of heavy-duty foil on top of each other, then fold them in half to form a rectangle. Fold up 2 inches on each side, neatly folding in the corners to form a low-sided box. Brush the foil with olive oil and set the fish on the foil. Season with salt and pepper and spoon 1/3 cup of the vinaigrette on each fillet. Using 2 long spatulas, set the foil package on a medium-hot grill and cook for about 15 minutes, or until the fish is just cooked through. Alternatively, roast the foil package on a cookie sheet in the oven for about 20 minutes. Transfer to a platter and serve with Braised Endives.