In a large skillet, heat the olive oil over medium heat. Add the ground chicken and cook until browned, about 5-7 minutes, breaking it apart with a spatula as it cooks.
Stir in the garlic powder, onion powder, smoked paprika, salt, and black pepper. Cook for an additional 1-2 minutes until the spices are fragrant.
Reduce the heat to low and add the hot honey, soy sauce, and rice vinegar to the skillet. Stir well to combine and cook for another 2-3 minutes until heated through.
To assemble, take a lettuce leaf and spoon a generous amount of the hot honey chicken mixture into the center. Top with chopped green onions, shredded carrots, and cilantro if using.
Squeeze fresh lime juice over the wraps before serving. Enjoy immediately.