In a medium bowl combine beef, tomatoes, lemon peel, 1/2 teaspoon salt, and 1/4 teaspoon pepper; mix lightly but thoroughly. Shape into four 1/2-inch-thick patties. Grill patties on the rack of an uncovered grill directly over medium heat for 14 to 18 minutes or until an instant-read thermometer inserted in side of patty registers 160 degrees F., turning once.
Meanwhile, in a small bowl combine mayonnaise dressing, basil, and jalapeno pepper; mix well. For the last 1 to 2 minutes of grilling, place buns, cut sides down, on grill rack to toast. Top bottom halves of buns with burgers. Top with mayonnaise dressing mixture and arugula. Add bun tops. Makes 4 servings.