1. Heat 2 teaspoons oil in a large nonstick skillet over medium heat. Add mushrooms; sauté 5 minutes or until tender, stirring occasionally. Place mushrooms in a large bowl. Heat remaining 1 teaspoon oil in pan over medium-high heat. Add turkey, garlic, and ginger to pan; cook 6 minutes or until turkey is browned, stirring to crumble. Add turkey mixture, onions, and water chestnuts to mushrooms in bowl; stir well.
2. Spoon 1/2 cup turkey mixture into each lettuce leaf. Combine hoisin, soy sauce, rice vinegar, Sriracha, and salt in a small bowl, stirring with a whisk. Serve sauce with lettuce cups.