Preheat the oven to 350 ⁰F (180 °C).Trim the majority of the fat off the lamb and clean the bones if needed. Season both sides of the rack with salt and pepper.Heat vegetable oil and butter in a large skillet over high heat, then sear the lamb until browned on all sides. Remove the lamb from the pan and set aside in a baking dish.Combine breadcrumbs, lemon zest, garlic, mint, parsley, rosemary, salt, and pepper in a bowl. Drizzle olive oil over the breadcrumb mixture, and mix until breadcrumbs are thoroughly coated.Spread the Dijon mustard over the browned rack of lamb that was set aside, take the breadcrumb mixture and press it onto the rack of lamb until it sticks and forms a crust.Roast the rack of lamb on the top rack of the oven. For medium-rare, bake for about 10 minutes or until meat thermometer reads about 60 °C (140 °F). Remove from the oven. Cover with aluminum foil and let rest a few minutes before slicing. Carefully cut into double chops, or single chops. Serve with herb roasted baby potatoes, asparagus, or other appropriate sides.