How to Make It
Preheat the oven to 400°. In a small bowl, combine 1/4 cup of the olive oil with the lemon juice. Pour half of the mixture over the lamb chops and let stand for 10 minutes.
Heat a large skillet until hot to the touch. Add the remaining 1 tablespoon of olive oil. Drain the lamb chops and season with salt and pepper. Add the lamb chops to the skillet and cook them over moderately high heat, turning once, until lightly browned, about 5 minutes. Transfer the lamb chops to a baking pan and roast them for 7 minutes for medium meat. Transfer the lamb chops to plates and keep warm.
Pour off all but 1 tablespoon of the fat from the skillet. Add the asparagus and cook over moderately high heat until crisp-tender, about 2 minutes. Add the arugula and cook just until barely wilted, about 1 minute. Add the remaining half of the lemon and olive oil mixture along with any accumulated juices from the lamb and bring to a simmer. Season the vegetables with salt and pepper and transfer them to the plates with the lamb. Scatter the Parmesan over the lamb and vegetables and serve.