Blend the llama and ground beef in a large bowl, being careful not to over blend as that will create a denser burger. Add the egg, bread crumbs, lemon juice, thyme, rosemary, feta, and salt and pepper, to taste. Mix well and form into 8 equal round patties, no more than 3/4-inch thick. Refrigerate for 30 minutes, allowing the ingredients and flavors to blend together.
Heat the grill to medium-high heat.
Add the burgers to the grill and cook until desired doneness is achieved, about 6 to 8 minutes per side. Remove and arrange on serving plates over sliced tomatoes. Drizzle with balsamic vinegar and garnish with chopped scallions.