Heat 1 tablespoon of the oil in a medium saucepan over medium-high heat; reduce heat to medium. Add pancetta and cook and stir for 5 minutes. Add garlic; cook and stir for 1 minute. Add lentils and chicken stock. Bring to boiling; reduce heat. Simmer, covered, for 25 to 30 minutes or until tender, adding additional stock if necessary. Season to taste with salt and pepper and set aside. Heat remaining oil in a medium skillet over medium-high heat. Add the mushrooms and cook and stir for 6 minutes or until browned. Season to taste with salt and pepper and fold into lentil mixture.
Place arugula in a food processor. With processor running, slowly add the olive oil. Add the walnuts and pulse until just chopped. Season to taste with salt and pepper.
Preheat oven to 475°F. In a large skillet place duck breasts, fat side down, and heat to medium. Cook about 15 minutes or until fat is almost gone. Remove duck from pan, reserving fat in pan. Turn heat to medium-high. Season duck and pork with salt and pepper. Add pork to hot pan and sear on all sides until browned. Place pork in a shallow baking pan and roast for 15 to 20 minutes or until an instant-read thermometer inserted in the pork registers 145°F. Remove; cover and set aside. Pour off all but 2 tablespoons fat from skillet.
Place duck, fat side down, in the skillet and cook until crisp, about 3 minutes. Turn and cook for 15 to 17 minutes more or until an instant-read thermometer inserted into duck registers 160°F. Remove duck from skillet to a plate; cover and set aside. Pour off all but 1 tablespoon fat from skillet. Add shallot and sherry to skillet. Return to medium heat. Scrape up any browned bits. Add beef stock to skillet. Bring to boiling; reduce heat. Boil gently, uncovered, for 6 to 8 minutes or until reduced by about half. Whisk in butter and season with salt and pepper.
Add pesto and lentils to each plate. Thinly slice the duck and pork and arrange on top of lentils. Spoon pan sauce over all and top with greens.