In a small skillet, heat the corn oil over medium heat. Add the onions and sweat, being careful not to brown them. Cook until onions are translucent and tender, about 5 minutes. Remove from heat and cool. While the onions are cooling make the aoili. In a small bowl combine all the ingredients and stir. Set aside. In a large bowl, combine the ground turkey, hatch chiles, cumin, oregano, garlic and salt. Add the onions and the oil (scraping the skillet to get all the oil and onions). Mix until thoroughly combined. Divide the mixture into 4 equal portions and pat out into 4 patties. Scrape and oil your grill and pre heat to medium high and add the burgers. Cook until burger easily releases from grill, about 3 - 4 minutes. Flip and cook on the other side and cook until the patties reach an internal temperature of 165 degrees.

Remove turkey burgers from the grill and add the buns to toast lightly if desired. Top burgers with lettuce and lime aoili.