Rinse and pat dry the lamb loin chops. In a bowl or plastic bag toss the loin chops with the rosemary, lavender, sea salt, black pepper, minced garlic, and the pieces of orange peel to thoroughly coat. Let sit in the fridge for at least a couple hours or overnight. You can skip this step if you don't want to wait for the dry marinade, they will still be very flavorful.
Preheat your grill to high heat. Slice all of your blood oranges in half and discard the orange peel from the lamb loin chops. Allow the lamb loin chops to come to room temp while the grill preheats.
Once the grill is hot grease the grates with whatever you like, I usually use lard or ghee. Immediately place the loin chops on the grill and allow to grill for 3 minutes then turn them about 45 degrees (we aren't flipping them yet we are just getting the hash grill marks on the meat.) and allow to grill another 2 minutes. Flip the loin chops and squeeze one of blood orange halves over the meat and grill for 3 minutes. Turn them 45 degrees again for the grill marks and squeeze another blood orange half over them, grill for 2 more minutes. This cooking time is for medium rare but you can cook them longer if you want them cooked more.
Immediately remove them from the grill and allow them to rest for 10 minutes. While they're resting keep your grill on high heat and clean off any bits off of the grates and make sure you're grill is still good and hot. If needed grease the grates again and add all of the remaining blood orange halves (there should be 4) onto the grill. Let grill for 3 minutes and then carefully wiggle them and take them off the grill without ripping off any flesh of the orange, turn them 90 degrees and grill for another 3 minutes.
Take them off the grill and serve the lamb loin chops with a drizzle of olive oil and a grilled orange half.