Bring a large pot of water to a rolling boil. Add the spaghetti and cook 5 minutes. Add the asparagus and cook an additional 4 minutes, or until the pasta is al dente. Drain.
While the pasta cooks, prepare the sauce: Add the avocado, 2 tablespoons of olive oil, garlic, lemon juice, lime, juice, and fresh herbs to a food processor or blender. Process on high for 20-30 seconds, or until smooth. Scrape into a small bowl and stir in the sour cream. Set aside.
Heat the remaining tablespoon of olive oil in a large pan set over medium heat. Add the shallot and cook 2-3 minutes, or until soft. Add the peas and arugula cook another 2-3 minutes, or until the arugula is wilted. Turn off the heat and stir in the cooked spaghetti, asparagus, and sauce. Stir to combine; season with salt and pepper.