GRILL DIRECTIONS: In small bowl, combine all gremolata mayonnaise ingredients; blend well. Set aside.
Heat grill. Place 1 chicken breast half, boned side up, between 2 pieces of plastic wrap or waxed paper. Working from center, gently pound chicken with flat side of meat mallet or rolling pin until about 1/4 inch thick; remove wrap. Repeat with remaining chicken breast halves. Brush chicken breast halves with 1 tablespoon of the oil; sprinkle with salt and pepper.
When ready to grill, place chicken on gas grill over medium heat or on charcoal grill 4 to 6 inches from medium coals. Cook 10 to 16 minutes or until chicken is fork-tender and juices run clear, turning once.
Meanwhile, brush zucchini and onion slices with remaining tablespoon oil; place on grill. Cook about 10 minutes or until tender, turning occasionally. To toast buns, place cut sides down on grill during last 2 to 4 minutes of cooking time.
Spread 1 tablespoon gremolata mayonnaise on bottom half of each bun. Top with lettuce. Place grilled vegetables evenly onto lettuce. Top each sandwich with chicken breast half, 1 tablespoon gremolata mayonnaise and top half of bun.