Whisk the sauce. In a small bowl, whisk soy sauce, honey, rice vinegar, sesame oil, water, cornstarch, and sriracha.
Set aside. The cornstarch will help the sauce thicken and glaze the chicken.
Prep the lettuce. Separate and wash the leaves. Pat them very dry, then chill in the fridge. Cold, crisp leaves make better wraps and hold up to the warm filling.
Cook the chicken. Heat oil in a large skillet over medium-high.
Add the chicken and break it up with a spatula. Cook until no longer pink and lightly browned at the edges, about 6–8 minutes. Season with a pinch of salt and pepper.
Add aromatics and veggies. Stir in garlic, ginger, bell pepper, and carrots.
Cook 2–3 minutes until fragrant and slightly tender. Add water chestnuts if using.
Sauce it up. Give the sauce a quick stir and pour it into the skillet. Stir constantly for 1–2 minutes until glossy and thick.
If it gets too thick, add a splash of water; if too thin, simmer another minute.
Finish and taste. Stir in green onions and a squeeze of lime. Taste and adjust: more soy for salt, honey for sweetness, vinegar for brightness, or chili for heat.
Assemble. Spoon the teriyaki chicken into lettuce leaves. Top with sesame seeds, herbs, radishes, and extra green onions.
Serve with lime wedges.