PREHEAT a grill to medium (350 to 375 F)
MAKE THE POTATOES: Put the potatoes in a large saucepan with enough water to cover. Lightly salt the water. Bring to a boil and cook until the potatoes can be pierced with the tip of a knife but are not completely tender, 9 to 10 minutes. Drain. When cool enough to handle, cut the potatoes in half lengthwise and toss with the olive oil and salt and black pepper to taste..
MAKE THE PESTO: In a food processor, combine the arugula, almonds, walnut oil, lemon zest and juice, garlic, salt, and cayenne. Process until smooth.
Grease the grill rack. Place the chops and potatoes on the greased rack over direct heat. Cover and grill the chops, turning once, for 12 to 14 minutes for medium-rare (145°F) or 15 to 17 minutes for medium (160°F). Grill the potatoes, turning once, for 10 minutes, or until they are tender and have grill marks.
Serve the lamb chops with the pesto and grilled potatoes.