Rub venison 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, and 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 1/2 of the dressing mixture over sliced and cooled venison, and toss to coat. Refrigerate for 1 hour.
In a large bowl, toss together lettuce, radishes, cilantro and red onion. Drizzle reserved dressing over, and lightly toss again. Mound lettuce mixture on plates, and top with marinated venison.