Whisk hoisin sauce, soy sauce, rice vinegar, Sriracha, and sesame oil in a small bowl. Set aside.
Heat oil in a large skillet over medium heat. Add onions and cook for 5 minutes until soft. Then, stir in garlic and ginger and cook for 1 minute more until fragrant.
Add ground chicken and cook until opaque and mostly cooked through. Break up the meat with a wooden spoon.
Pour in the sauce and cook for 1 to 2 minutes more, until the sauce reduces slightly and the chicken is cooked through completely. Turn off the heat and stir in water chestnuts. Taste the mixture and season with salt and pepper, if needed.
While the chicken cooks, make the peanut sauce by whisking all ingredients together in a small bowl. For a thinner sauce, add water 1 tablespoon at a time until desired consistency is reached.
Serve the chicken mixture with lettuce leaves. Spoon about ¼ cup into the center of each leaf. Top with crushed peanuts and green onions. Serve with peanut sauce.