Arrange the tuna on a lightly oiled grilling tray or broiler pan. Place 1/4 cup of the Mustard Dressing in a small bowl. Brush some dressing over the fish. Grill or broil, uncovered, for 5 minutes.
Turn the fish and arrange the star fruit alongside it on the grilling tray. Brush the fish and star fruit lightly with the dressing. Return to the grill. Cook for 3 to 6 minutes longer, or until the fish flakes easily with a fork.
Combine the lettuce and cucumber in a large salad bowl. Add the remaining dressing and toss to coat well. Divide the salad evenly among 4 dinner plates. Place 1 piece of tuna on the center of each salad. Arrange the star fruit slices around each salad plate. Sprinkle with green onions.
Combine the mayonnaise, lime juice, mustard, dill, and paprika in a small bowl and mix well. Chill until ready to use.