Bring a pot of water to a rapid boil and season generously with salt. Cook the pasta al dente according to the packaged instructions. Reserve 1 cup of pasta water.
While the pasta is cooking, melt 1 tablespoon of butter in a large skillet over medium heat. Add the garlic and sauté for 1 minute. Add asparagus to the skillet and sauté until tender, stirring occasionally for 3 to 4 minutes. Remove from skillet.
Add the remaining butter to the skillet. Then stir in the heavy cream and simmer until it thickens, 5 to 7 minutes.
Once the cream thickens, remove the pasta directly from the pot (do not rinse) and place it in the pan. Stir in ⅓ cup pasta water. Add more, 1 tablespoon at a time, until you reach your preferred consistency. Add Parmesan, lemon zest, and lemon juice and toss to combine. Then stir in the asparagus. Season with salt and pepper to taste.