Preheat an outdoor grill for high heat and lightly oil the grate.
Mix ground turkey, onion, egg substitute, basil, horseradish, soy sauce, pepper, and garlic in a large mixing bowl; form into 4 patties.
Cook the turkey burgers on the preheated grill until no longer pink in the center and the juices run clear, about 6 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Serve on buns with lettuce and tomato.