Combine ground lamb, basil, sun-dried tomatoes, garlic, salt, and pepper in a bowl and mix well using your hands. Form into 4 equal-sized patties.
Heat a skillet over medium-high heat. Add olive oil and allow to get hot. Add lamb burgers. Cook 5 minutes and flip burgers. Continue cooking until an instant-read thermometer inserted into the center reads at least 160 degrees F (71 degrees C), about 5 minutes more.
