Bring 4 quarts water to a boil in a large pot for the pasta.
Meanwhile, heat 1 tablespoons of the butter in a 12-inch nonstick skillet over high heat until beginning to brown. Add the chicken, break up any clumps, and cook without stirring until beginning to brown, about 1 minute. Stir the chicken and continue to cook until almost cooked through, about 2 minutes longer. Transfer the chicken to a medium bowl, cover with foil, and set aside.
Add 1 tablespoons more of the butter, the leek, and 1/4 teaspoons salt to the skillet and cook over high heat until browned on the edges, 2-3 minutes. Stir in the garlic, thyme and flour and cook until fragrant, about 30 seconds. Add the chicken broth and wine, bring to a simmer, and cook over medium heat until the sauce has thickened slightly and reduced to 1 1/4 cups, about 15 minutes.
Meanwhile, stir 1 tablespoons salt and the asparagus into the boiling water and cook, stirring often, until the asparagus are crisp-tender, about 1 minute (do not overcook). Using a slotted spoon, transfer the asparagus to a paper towel-lined plate and set aside.
Return the water to a boil, stir in the pasta, and cook, stirring often, until the pasta is al dente. Reserve 1 cup of the pasta cooking water, then drain the pasta and return it to the pot. Return the chicken to the skillet along with the remaining 2 tablespoons butter, the Parmesan, lemon zest and lemon juice. Continue to simmer until the chicken is cooked through, about 1 minute.
Pour the chicken and sauce mixture over the pasta and add the asparagus and basil. Toss gently to combine, adding the reserved pasta cooking water as needed to loosen the sauce. Season with salt and pepper to taste and serve, passing additional Parmesan separately.