In a large skillet, heat the vegetable oil over medium-high heat. Add the chopped onion and sauté for about 2-3 minutes until translucent.
Stir in the minced garlic and ginger, cooking for another minute until fragrant.
Add the ground chicken or turkey to the skillet, breaking it apart with a spatula. Cook until browned and fully cooked through, about 5-7 minutes.
Stir in the chopped mushrooms and red bell pepper, cooking for an additional 3-4 minutes until the vegetables are tender.
In a small bowl, mix together the soy sauce, hoisin sauce, rice vinegar, sesame oil, and water. Pour the sauce over the cooked meat and vegetables, stirring to combine.
Add the chopped water chestnuts and sliced green onions, cooking for another 2 minutes.
To serve, spoon the chicken mixture into the lettuce leaves and enjoy as wraps.