For the filling: Brown the turkey in the oil in a large saute pan over medium-high heat until no longer pink. Add the mushrooms, scallions, garlic and water chestnuts, and cook until the mushrooms soften. In a small bowl, mix the soy sauce, brown sugar and vinegar, pour over the turkey mixture and cook 1 minute. Remove from the heat.
For the drizzling sauce: In a small bowl, whisk together the soy sauce, vinegar, honey, mustard, Sriracha, sesame oil and 1/4 cup water.
Serve the turkey mixture with the lettuce leaves, drizzling sauce and vegetables for lettuce wrap assembly.