For the Mint Relish
Combine all ingredients in bowl. Let sit at room temperature until needed. (Makes 1½ cups.)

For the Lamb
Line large roasting pan with aluminum foil. Adjust oven rack to lower-middle position, place prepared pan on rack, and heat oven to 425 degrees.

Pat lamb dry with paper towels and season with salt and pepper. Heat 1 tablespoon oil in 12-inch skillet over medium-high heat until just smoking. Place 2 racks in skillet, fat side down with ribs facing outward, and cook until well browned, about 5 minutes.

Using tongs, stand racks up in skillet, leaning them against each other, and brown bottoms, about 2 minutes; transfer to large platter. Repeat with remaining 1 tablespoon oil and remaining 2 lamb racks; transfer to platter. (Seared lamb can be held at room temperature for up to 1 hour before finishing in the oven.)

Transfer lamb racks to hot pan in oven and roast until lamb registers about 125 degrees (for medium-rare), 12 to 15 minutes. Transfer lamb to carving board, tent loosely with foil, and let rest for 5 to 10 minutes. Cut lamb racks into individual chops by slicing between each rib and serve with mint relish.