For the lamb: Combine all the ingredients for the marinade, except the lamb, and whisk together to form a thick paste. Slather on the lamb chops. Marinate the chops at room temperature up to 2 hours or in the refrigerator for up to 2 days.
For the tzatziki: Combine all the ingredients. Season with more salt, if necessary. Let sit for at least 1 hour at room temperature before serving.
Preheat the grill to medium. When the grill is hot, brush the grates with a wire grill brush to loosen any crud. Wipe the grates with an oiled side towel to pick up any loose soot or crud.
If the lamb was in the refrigerator, let it come to room temperature before grilling.
Arrange the lamb chops on the grill. Do not move the chops for 2 to 3 minutes to allow lovely grill marks to form. Rotate the chops 90 degrees to create cross-hatch grill marks, and grill for another 2 to 3 minutes. Flip the chops and repeat the process. Remove the chops from the grill to a platter and let rest for 5 to 10 minutes before serving.
For the salad: Toss the arugula with the lemon juice, big fat finishing oil, and salt. Adjust the seasoning, if necessary, and sprinkle with the crumbled feta. Divide the salad among 4 serving plates and top with a lamb chop. This will slightly wilt the salad. Drizzle with big fat finishing oil and top with a dollop of tzatziki.