Rub duck with 1 tablespoon olive oil. Heat a large skillet over medium-high heat and brown meat evenly on both sides, but not past medium-rare. Allow to cool, then slice diagonally into thin strips. Place in a medium bowl.
Prepare dressing. In a medium bowl, whisk together fish sauce, sugar, lemon juice, garlic, mint, red pepper flakes and black pepper. While whisking, add remaining oil in a thin stream until emulsified. Pour one-half of the dressing mixture over sliced and cooled duck and toss to coat. Refrigerate for 1 hour.
In a large bowl, toss together lettuce, sliced radishes, cilantro leaves, onion and remaining dressing. Remove sliced duck from bowl and shake off excess dressing. Gently toss duck with salad mixture. Mound salad on plates.