Combine sriracha and oil in a 12-inch skillet over medium-high heat. Cook 3 minutes or until mixture begins to bubble.
Add the onion and ginger. Stir for a minute.
Add the turkey. Raise the heat to high. Cook 6 minutes, stirring until the meat is scattered throughout the pan. Keep stirring. So long as nothing's burning, keep the heat cranked and the turkey moving.
When the turkey is cooked through and slightly crisped, turn off the heat. Toss in the green onions, the lime juice, the peanuts, the fish sauce, and the thai chiles. Fold to combine.
Divide the turkey mixture evenly among the lettuce leaves. Top each leaf with 2 tablespoons cucumber, 2 tablespoons carrot, and 1 tablespoon cilantro.
Serve with fresh lime wedges, if desired.