Make the sauce: In a small bowl, whisk together hoisin sauce, soy sauce, rice wine vinegar, Sriracha, and sesame oil.
In a large skillet over medium-high heat, heat olive 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. Add celery for last 3 mins.
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 green onions. Season with salt and pepper.
Spoon rice, if using, and a large scoop (about ¼ cup) of chicken mixture into center of each lettuce leaf. Sprinkle cashews and sesame seeds over top. Serve immediately.
