In a small bowl, whisk together the olive oil, minced garlic, finely chopped rosemary, sea salt, and black pepper.
Pat the lamb chops dry with a paper towel and rub the herb mixture evenly over both sides.
Allow the lamb to marinate at room temperature for 15 minutes while you preheat your grill or grill pan to medium-high heat.
Trim the woody ends off the asparagus and lightly mist with a tiny bit of oil if desired.
Place the lamb chops on the hot grill and cook for 4-5 minutes per side for medium-rare, or until they reach your preferred doneness.
During the last 4 minutes of cooking, place the asparagus on the grill, turning occasionally until tender and slightly charred.
Remove the lamb and asparagus from the heat and let the meat rest for 5 minutes.
Squeeze fresh lemon juice over the lamb and vegetables just before serving for a bright finish.