In a small bowl, combine the lime juice, cilantro, fish sauce, sugar, ginger, garlic, and chile and let sit for at least 10 minutes.
Meanwhile, bring a large pot of well-salted water to a boil. Add the rice noodles and stir immediately. Cook the noodles, stirring frequently, until just tender, about 4 minutes. Drain and rinse the noodles with cold water until cool to the touch.
In a large salad bowl, combine the noodles with the lettuce, carrot, cucumber, radishes, and mint leaves. Toss the salad with the dressing and garnish with the peanuts.