In a small bowl, mix the sauce ingredients. Set aside.
In a large skillet, heat the avocado oil over medium heat, until shimmering. Add the bell peppers and mushrooms. Saute for 2-4 minutes, until vegetables soften slightly and any moisture evaporates. Remove from the skillet and set aside.
Heat the same skillet over medium-high heat. (Add more oil if needed.) Cook ground chicken for 5 minutes.
Add the onions, garlic, and ginger. Continue cooking for 3-5 minutes, until the chicken is cooked through.
Return the mushrooms and bell peppers to the skillet. Add the water chestnuts (if using). Stir in the sauce. Bring to a gentle boil, then simmer for 2 minutes.
Separate the leaves from the head of lettuce. Fill the leaves with chicken filling, about 2-3 tablespoons per lettuce wrap.
Top with green onions, sesame seeds, and peanuts, if desired.