In a small saucepan combine the sugar and 2 tablespoons water. Place over medium heat and bring to a simmer, stirring occasionally to dissolve the sugar. Add the lemon segments and simmer for another 2 minutes. Turn off the heat and cool the lemons in the liquid. Using a slotted spoon, remove the segments from the liquid and reserve both for later use.
In a medium bowl, whisk together the mustard and 2 tablespoons of the reserved lemon liquid. Whisk in the olive oil, basil and 1/8 teaspoon of the salt. Reserve half of the dressing for the fish. Add the arugula, olives and reserved lemon segments to the dressing but do not toss. Set aside.
Heat a grill pan over medium-high heat. Dry the fish well using paper towels and sprinkle with 1 teaspoon of the salt and the olive oil. Grill the steaks until golden brown and the fish release easily from the pan, 3 to 4 minutes per side depending on the thickness of the steaks. Toss the salad in the dressing and add the remaining 1/4 teaspoon salt. Place a piece of fish on each plate and top with some of the salad. Spoon the reserved dressing around the fish.
In America, I suggest using tuna steak. In Italy, swordfish was readily available.