Mix first 4 ingredients in large bowl until blended. Mix in pepper. Shape half of meat mixture into eight 1/2-inch-thick patties. Shape remaining meat mixture into four 1-inch-thick patties. (Can be made 8 hours ahead. Cover and chill.)
Prepare french fries according to package instructions.
Prepare barbecue (medium-high heat). Grill patties to desired doneness, topping with cheese for last minute of cooking, about 4 minutes per side for medium-rare 1/2-inch-thick patties, and about 6 minutes per side for medium-rare 1-inch-thick patties. Place burgers on bottom halves of buns. Top with lettuce, tomatoes and upper halves of buns.
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