Rub the lamb with 1/4 cup of the olive oil and season both sides with salt and pepper. Arrange the lamb fat-side up on a roasting pan and roast 15 minutes. Lower the temperature to 350 degrees F and roast until golden brown and a meat thermometer inserted in the center of the lamb reads 130 degrees F, another 25 to 30 minutes.
While the lamb roasts, make the chimichurri. Combine the mint, parsley, oregano, garlic, serrano and 1 teaspoon salt in a food processor and blend. With the machine running, drizzle in the lime juice and remaining 1/2 cup olive oil and process just until fully combined. Taste and season with salt and pepper.
Remove the lamb from the oven and allow it to rest for 10 minutes. This will allow the juices to redistribute and the lamb will continue to cook. The temperature should read 140 degrees F. Slice the lamb against the grain and add to a platter. Top with some of the chimichurri and serve the remaining sauce alongside the meat at the table.