In a blender, combine the lemon juice, garlic, pine nuts, parmesan, basil, arugula, salt, pepper and olive oil until smooth. Adjust the seasoning with salt and pepper.
Cover the chicken in half of the pesto and marinate for at least 4 hours and up to overnight.
Preheat the oven to 400°F.
Arrange the chicken on a baking sheet, drizzle with olive oil and sprinkle with salt and pepper. Roast until cooked through, 15-20 minutes.
Bring a large pot of salted water to a boil for the pasta. Add the pasta, stirring to prevent clumps. Cook to al dente, according to package instructions, strain and return to the pot, drizzled with oil to prevent sticking.
Boil a large pot of salted water for the green beans. Prepare an ice bath by filling a large bowl with cold water and ice. When the water boils, add the green beans for 2-4 minutes then immediately transfer to the ice bath to stop the cooking process. Remove from the ice bath after 1-2 minutes.
Toss the penne with the remaining pesto and divide between plates. Top with chicken and green beans and sprinkle with shaved parmesan to serve.