To prepare sauce, combine first 5 ingredients, stirring with a whisk.
To prepare noodles, heat oil in a large nonstick skillet over medium-high heat. Add mushrooms, carrot, and garlic; sauté 2 minutes. Add sauce and tofu; cook 1 minute. Stir in coconut milk; cook 2 minutes. Stir in lettuce and next 5 ingredients (lettuce through noodles); cook 1 minute. Serve with lime wedges.