Grilled Lobster and Potatoes with Basil Vinaigrette

Name: Grilled Lobster and Potatoes with Basil Vinaigrette
Ingredients: 4 (1 1/4- to 1 1/2-pound) live lobsters; 2 pounds small (1 1/2- to 2-inch) boiling potatoes (preferably yellow-fleshed); 3 tablespoons red-wine vinegar; 5 tablespoons fresh lemon juice; 3 garlic cloves, minced; 1/2 teaspoon dried hot red-pepper flakes, or to taste; 1 teaspoon sugar; 1/2 teaspoon salt; 2/3 cup extra-virgin olive oil; 1/2 cup chopped fresh basil; 1/2 pound baby arugula (about 10 cups loosely packed); Accompaniment: lemon wedges