Cook the pasta in salted water according to package instructions. Add the asparagus to the pot during the last 3 minutes of cooking time.
Reserve 1/4 cup of pasta cooking liquid.
In small pot, combine the heavy cream, butter and 1/2 teaspoon salt and 1/4 teaspoon pepper over medium-high heat. Bring to a simmer and cook, stirring, until thick enough to coat a spoon, about 4 minutes. Remove from the heat and stir in the lemon zest and juice.
Place the pasta and asparagus back into the pot you cooked it in along with the chicken.
Pour the cream sauce over the pasta mixture and toss to coat evenly, adding pasta water if needed to thin the sauce. Stir in the parmesan cheese. Alternatively, you can toss just the pasta with the sauce and arrange the chicken and asparagus over the top of the pasta.
Add more salt and pepper to taste if needed. Garnish with chopped parsley and lemon slices if desired.