Preheat your grill or grill pan to medium-high heat.
In a small bowl, combine 0.5 tbsp of the olive oil with the dried rosemary, dried thyme, minced garlic, 0.25 tsp of the sea salt, and the black pepper.
Rub the herb and garlic mixture evenly over all sides of the lamb loin chops, pressing gently so the herbs adhere.
Trim the woody ends off the asparagus spears and toss them in a bowl with the remaining 0.5 tbsp of olive oil and 0.25 tsp of sea salt.
Place the lamb chops on the hot grill and cook for 4 to 5 minutes per side for medium-rare, or until they reach your preferred level of doneness.
While the lamb is cooking, place the asparagus spears on the grill or in a hot pan, turning occasionally until they are tender and slightly charred, about 5 to 7 minutes.
Remove the lamb chops from the grill and let them rest on a plate for 5 minutes to allow the juices to redistribute.
Drizzle the lemon juice over the roasted asparagus and serve immediately alongside the rested lamb chops.