Whisk together hoisin sauce, soy sauce, rice wine vinegar, Sriracha and sesame oil in a small bowl. Set aside.
In a large skillet over medium-high heat, heat oil. Add onions and cook until soft, 5 minutes, then stir in garlic and ginger and cook until fragrant, 1 minute more. Add ground chicken and cook until opaque and mostly cooked through, breaking up meat with a wooden spoon.
Pour in sauce and cook 1 to 2 minutes more, until sauce reduces slightly and chicken is cooked through completely. Turn off heat and stir in water chestnuts. Taste mixture and season with salt and pepper, if needed.
Make peanut sauce by whisking together all ingredients in a small bowl. For a thinner sauce, add water 1 Tablespoon at a time to create the desired consistency.
Serve chicken mixture with lettuce leaves and spoon about 1/4 cup into center of each leaf. Top with crushed peanuts and green onions. Serve with peanut sauce.