Heat grill to medium.
Rub the lamb with the oil and garlic and season with 1 teaspoon salt and 1/2 teaspoon pepper. Grill to desired doneness, 4 to 5 minutes per side for medium-rare. Let rest 5 minutes, then cut into bite-size pieces.
Meanwhile, in a large bowl, whisk together the mayonnaise, lemon juice, cinnamon, cayenne, and 1/2 teaspoon salt.
Use a vegetable peeler to cut the carrots into long, thin strips. Add the carrots, mint, raisins, and scallions to the dressing and toss. Serve with the lamb.
Shortcut: If you're tight on time, you can coarsely grate the carrots in a food processor instead of peeling them into long strips.