Roughly chop the garlic and then sprinkle the salt on top. Using both the sharp edge and the flat side of the knife blade, crush the garlic and salt together to create a paste. Add the remaining seasoning ingredients and chop them together.
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Lightly brush or spray the chops on both sides with oil. Spread half of the seasoning mixture on both sides of the lamb chops. Allow the chops to stand at room temperature for 15 to 30 minutes before grilling.
Put the cut potatoes in a medium bowl. Drizzle 2 tablespoons of oil over the top and add the remaining half of the seasoning mixture. Stir the potatoes to coat them evenly.
Brush the cooking grates clean. Grill the potatoes over direct medium heat, with the lid closed as much as possible, until tender, 15 to 20 minutes, turning every 5 minutes. Remove from the grill and keep warm while you grill the lamb.
Grill the lamb chops over direct medium heat, with the lid closed as much as possible, until cooked to your desired doneness, about 8 minutes for medium rare, turning once or twice (if flare-ups occur, move the chops temporarily over indirect heat). Remove from the grill and let rest for 3 to 5 minutes. Serve warm with the potatoes.